New Home for Fibonacci and Descartes
Ms. Leckman decided that the Math Club mascots, Fibonacci and Descartes, had outgrown their 10-gallon home, so this weekend she picked up a 15-gallon aquarium at a flea market. Oliver and Suzanne have been assigned the task of setting up the new aquarium. They have been instructed to fill it exactly three-quarters of the way to the top. Fibonacci and Descartes will be transferred with some of the water from their current environment to help them adjust to their new home. Unfortunately, Suzanne and Oliver can not find a clean bucket for carrying water to the aquarium. All they can find are two eight-ounce glasses. Working from the sink to the left of the aquarium stand, Suzanne takes 45 seconds to fill one glass and dump it into the aquarium. Working from the sink to the right of the aquarium, Oliver can fill one glass and dump it into the tank in 39 seconds.
If Suzanne and Oliver start at noon and keep working at these constant rates, what time will they complete their task? Which student will add the last glass of water?
Remember there are a number of ways to solve this – so be sure to explain and show how you arrived at your solution to obtain credit for this assignment.
12 comments:
POW NH
There are 128 ounces in 1 gallon
¾ of 15 gallons is 11.25 gallons
128 x 11.25= 1440 ounces to fill the tank
Oliver is 6 seconds ahead of Suzanne
84 seconds pass and there are 16 ounces in the tank
45 seconds later there will be 32 ounces.
Oliver is now 12 seconds ahead of Suzanne
45 seconds in the future there is 28 ounces and Oliver is 18 seconds ahead
Another 45 seconds later there is a total of 64 ounces in the tank and Oliver is 27 seconds ahead.
Another 45 seconds later there is 80 ounces in the tank and now Oliver will always be 18 seconds ahead of Suzanne.
Every other time she pours her glass. The other time he is 27 seconds ahead of her.
After 8 pours there will be 128 ounces (1 gallon) in the tank
After 88 pours there will be around 11 gallons in the tank which is 1440.
2 more pours will get them to exactly 11.25 gallons
By the end of the 92 total pours divided by 2 is 46, times 45 =2,070which = 34.5 minutes that will pass
P.O.W. …………………..C.H.
There are 128 ounces in a gallon.
Three fourths of fifteen gallons is 11.25.
128 times 11.25 equals 1440. This is the amount of ounces needed to fill the tank three fourths of the way.
Oliver will dump the first glass at 39 seconds. 6 seconds later Suzanne dumps her glass. After 45 seconds there is 16 Oz. in the tank and Oliver is 6 seconds into his next glass. After 90 seconds there will be 32 Oz. of water in the tank. Oliver is now 12 seconds into his next glass. 45 seconds later there is 48 Oz. Oliver is now 18 seconds into his next glass. 45 seconds later there is 64 Oz. in the tank and Oliver is 27 seconds into his next glass. 45 seconds later there is now 80 Oz. in the tank.
A pattern has now started where every other time that Suzanne pours her cup of water Oliver will be 18 seconds ahead. All the other times he will be ahead by 27. So now every 45 seconds another 16 Oz. goes into the tank. After eight pours there will be 1 gallon of water in the tank. So after 88 pours (44 pours for each of them) there will be 11 gallons in the tank. Another two pours for each of them will get the tank to exactly 11.25 gallons in the tank. If every two glasses of water into the tank took 45 seconds. There will be a total of 92 pours, so 92 divided by 2 is 46. So 46 times 45 is 2070 seconds. This is equal to 34.5 minutes.
E.K. POW
Data
15 gallon tank, filled ¾ of the way
2 cups
Oliver fills in 39 seconds
Suzanne fills in 45 seconds
1gallon is 128oz
Step 1
How many gallons must be filled?
¼ of 15gallons is 3.75
15-3.75=11.25
11.25 gallons must be filled.
Step 2
How long does it take for Oliver to fill a gallon?
39=8oz
128/8=16cups
39*16=624seconds
624/60=10.4 minutes
It takes Oliver 10minutes and 24seconds to fill 1gallon.
Step 3
How long does it take for Suzanne to fill a 1gallon?
45=8oz
128/8=16cups
45*16=720seconds
720/60=12minutes
It takes Suzanne 12minutes to fill 1gallon.
Step 4
How long does it take for them to both fill 1gallon?
12 minutes since there is 2 cups so they can work at the same time, but Oliver would have been 1.6(or 1minute 36 seconds) minutes into filling the next gallon.
Step 5
How long does it take each of them to fill 5 gallons?
Oliver
10.4*5=52minutes
Has an 8 minute extra start
Suzanne
12*5=60minutes
In 1 hour they would both have filled 5 gallons for a total of 10.
Step 6
How do you fill that extra 1.25gallon?
Oliver is always ahead of Suzanne and can fill the extra gallon (since only ¾ of the tank is being filled) so when she finishes her last gallon he got the old one.
The answer
In the end it takes 1 hour for ¾ of the tank to be full.
Oliver will add the last glass of water since he is always ahead of Suzanne.
J.K. POW May 2, 2008
First of all we want to figure out how many times 8 fluid ounces goes into ¾ of 15 gallons. There are 128 fluid ounces in a gallon. ¾ of 15 gallons is 11.25 gallons. The total number of fluid ounces in 11.25 gallons are 1440. Suzanne fills 8 fluid ounces in 45 seconds so 1440 / 8 is 180. That how many cups Suzanne and Oliver have to fill but we are just working with Suzanne right now. This means that 180 times Suzanne will take 45 sec. to fill the 8 fluid ounce glass. In other words 180 times 45 sec is how long it will take Suzanne to fill ¾ of the 15 gallon tank. 8100 sec or 135 minutes or 2 hours 15 minutes or 2.25 hours is how long it would take Suzanne to fill ¾ of the 15 gallon tank. This is how long Suzanne will take to fill the tank. But wait! Suzanne isn’t the only one who is filling the tank! Remember? Oliver is helping her.
Oliver fills the tank at a rate of 8 fluid ounces every 39 seconds. That means for Oliver to fill ¾ of the tank it would take him 117 minutes or 1 hour 57 minutes or 1.95 hours. They must both work the same amount. I have an idea. How about we try finding the average time it will take to fill 16 ounces? Let’s do it. 39 plus 45 divided by 2 equals 42 seconds. Let’s see how long it will take to fill that ¾ of the tank. This time it is 42 seconds to fill 16 ounces because they are both working. 90 times 42 equals 3780 seconds or 63 minutes or 1 hour 3 minutes or 1.05 hours.
It takes Suzanne and Oliver 1 hour 3 minutes to fill ¾ of the tank. They will finish at 1:03 p.m. Oliver will put in the last glass because he works faster than Suzanne so he will put one more than her. He can put more glasses into the time it takes them to fill ¾ of the tank.
POW
RB
Work
• 15*0.75=11.5 gallons to fill up
• 11.5*128= 1440 ounce to fill up
• 1440/8=180 cups/trips to do
• Every 84 seconds there is another 16 ounces in the bowl and, 6 and half rounds; Oliver is ahead by one glass
• There is 16 ounces in the bowl with Oliver ahead by 6 seconds. 32 ounces and Over is ahead by 12 seconds. 48 ounces and Oliver is 18 seconds ahead. 64 ounces and Oliver is 24 seconds ahead. 80 ounces and Oliver is 30 seconds a head. 96 ounces and Oliver is 36 seconds ahead. 120 ounces and Oliver is 3 seconds ahead and has taken a total of 270 seconds.
• 12*270=3240
• 3240/60=54
Answer
It will take Oliver and Suzanne 54 minutes to fill the tank ¾ of the way. Suzanne will add the last glass of water while Oliver almost puts his in the bowl because he is 36 seconds ahead, almost one more glass.
POW MR.
150*.75 =11.25 multiply 11.25 by 128 to convert gallons into ounces because 1 gallon =128 ounces
11.25 * 128 = 1440 ounces needed to fill ¾ of the tank
8/39= .201 or about .201 water poured per second
8/45= .177 or about .177 water poured per second
Oliver pours water at a rate of about .201 per second
Suzanne pours at a rate of about .177 per second
The LCM of 39 and 45 is 585
Oliver ounces per 585 seconds Suzanne ounces per 585 seconds
117.58 103.54
235.16 207.09
352.74 310.63
585*3= 1755 seconds or 29 minutes and 15 seconds
352.74+310.63= 663.37
This means when both pouring together they pour about 663.37 ounces in 29 minutes and 15 seconds
663.37 *2 = 1326.74 ounces poured
29.25*2 = 58.5 or 58 minutes and 30 seconds.
Suzanne will pour 16 ounces in the next 90 seconds
Oliver will pour 18 ounces in the next 90 seconds 1326+34= 1360 after another 90 seconds it will be 61 minutes and 30 seconds after the start and there will be 1394 ounces of the 1440 to be filled after another 90 seconds it will be 63 minutes from the start and 1428 of the 1440 filled Oliver will fill it next changing the total to 1436 Suzanne will fill the last cup and finish filling the tank at 63 minutes and 45 seconds
Last cup poured is Suzanne
Time of finish is 1:03 and 45 seconds
JW
First, I started to find the information needed to figure out the answer to the problem
8 ounces are in a cup
128 ounces are in a gallon.
That means that 16 cups in a gallon.
That means that 240 cups are in Mrs.Leckman’s new tank.
Only, you can’t do that, because ¾ of the tank need to be full.
¾ of 240 =90, so there needs to be 90 scoops in all to fill the tank with the appropriate amount of water.
To solve how many and in how much time they each make, 15x60/45 is the way I solve for Suzanne, and 15x60/39 is how I solve for Oliver, until the last part, and I just plug in the amount of time I want to go by with the 15.
12:00-12:15: Suzanne makes 20 cups, and Oliver makes 23 cups 23+20=43 Cups
12:15:12:30: Suzanne makes 20 cups, and Oliver makes 23 cups 23+20=43+43=86 Cups
12:30-12:31: Suzanne makes 1 cup, and Oliver makes 2 cups 1+2+86=89 cups
12:31-12:31.39, Suzanne makes 0 cups and Oliver makes 1 cup, ending at 90 cups.
It takes them approximately 32 Minutes, and Oliver puts the last cup in.
EMK
128 ounces in a gallon
8 oz in a cup
16 cups in a gallon
SUZANNE
45x16=720
720x15=10800
10800/.75=14400 seconds Suzanne will put the last glass in.
14400/60=240 minutes They will be done after 32 minutes.
240/60=4 hours I got this after dividing a lot of things.
OLIVER
39x16=624
624x15=9360
9360/.75=12480 seconds
12480/60=208 minutes
208/60=3.46 hours
3.46/4=.87
SV
How long it takes Suzanne- 14400 seconds
How long it takes oliver- 12480 seconds
14400/60- 240 minutes
12480/60- 208 minutes
Suzanne- 4 hours
Oliver- 3.46 hours
3.46/4 = .87 (rate)
Y=mx+b
Y=.87x
208.8 minutes
180.96 minutes
389.76/60=6.5
Suzanne and Oliver would finish at 6:30 pm
C.C.
Oliver and Suzanne will finish at 6:27 p.m. and Suzanne will poor in the last glass. I got my answer of the time by first finding out how many ounces are in a gallon which is 128 Oz. and then I multiplied 7 times 128 because I only have to fill ¾ of 10 gallons. Then for both of them I divided 896 by 2 then I multiplied 448 by the amount of time it took the two fill up and pour the 8 ounce glasses in the fish tank. After I divided the total amount for both Oliver and Suzanne by sixty then added both of the total times together and added the two the time of noon. Then I found out that Suzanne poored the last glass because it took her longer to fill up her portion of the tank.
D.E.
Oliver’s Progress (total) Suzanne’s progress (total) Total amount of tank filled
1. 117-24 1. 135-24 48 ounces
2. 234-48 2. 270-24 96 ounces
3. 351-72 3. 405-72 144 ounces
4. 468-96 4. 540-96 192 ounces
5. 585-120 5. 675-120 240 ounces
6. 702-144 6. 810-144 288 ounces
7. 819-177 7. 945-168 345 ounces
8. 936-201 8. 1080-192 393 ounces
9. 1053-225 9. 1215-216 441 ounces
10. 1170-249 10. 1485-264 489 ounces
On 6., Oliver has gotten 8 extra ounces because he refills 6 seconds faster than Suzanne and when those 6 seconds keep adding up to another 39 seconds, it means an extra cup.
11. 1287-273 11. 1620-288
12. 1404-297 12. 1755-312
13. 1581-321 13. 1890-336
14. 1698-353 14. 2025-360
15. 1875-377 15. 2160-384
16. 2052-401 16. 2295-408
17. 2229-425 17. 2430-432
18. 2346-449 18.
19. 2463-473 19. 929 ounces
83.8 hours
Suzanne
M.G. P.O.W
128 ounces = 1 gallon
New tank = 15 gallons
15/4 = 3.75 so ¾ of the tank is 11.25
11.25 gallons = 1,440 ounces
1,440/8 = 180 times to fill glasses to fill tank
180-16 = 164 times to fill glasses with new water
164/2 = 82 times to fill glasses with fresh water to fill tank
Oliver takes 39 seconds to fill one glass 39*82 = 3,198 seconds 3,198/60 = 53.3 minutes
Suzanne takes 45 seconds to fill one glass 45*82 = 3,690 seconds 3,690/60= 61.5 minutes
Suzanne and Oliver would take approximately 63 minutes to do the task considering it will take a little extra time to transfer Fibonacci and Descartes to their new tank.
So, they would finish a little after one o’clock.
Because of the way I did it, Oliver and Suzanne both took even shares, so Suzanne put the last amount of water in (because she took longer).
Extra Credit = 50% for Oliver and 50% for Suzanne
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