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Tom and Jerry are filling up 500 water balloons a piece. It takes Tom

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Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 22 Jan 2019, 18:48
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Question Stats:

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Tom and Jerry are filling up 500 water balloons a piece. It takes Tom 2 hours longer than Jerry to fill up 500 water balloons. Jerry can fill 50% more water balloons per hour than Tom. How many water balloons per hour can Jerry fill?

a. 125

b. 150

c. 180

d. 200

e. 250
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Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post Updated on: 27 Jan 2019, 21:40
Jazzmin wrote:
Tom and Jerry are filling up 500 water balloons a piece. It takes Tom 2 hours longer than Jerry to fill up 500 water balloons. Jerry can fill 50% more water balloons per hour than Tom. How many water balloons per hour can Jerry fill?

a. 125

b. 150

c. 180

d. 200

e. 250


Though i didn't get the answer at first, can someone validate this approach

Tom will take 2 hrs more than Jerry, Tom and Jerry are filling up 500 water balloons a piece, meaning they both will fill 500 balloons each

Jerry can fill 50% more water balloons per hour than Tom( difference between rate is given) -> This will mean that T was 10 balloons/hour Jerry would be 15 balloons/hour

Will just consider the options directly

Work = Rate * time

500/ time = Rate, Plug in values for hrs

a) Jerry = 125 balloons/hr, this means Tom would have been = 83.33 balloons/hr - > this is our Answer

Jerry can take x hours, then Tom will take x+2 hrs

J = 125 *4 = 500

T = 83.33 * 6 = 499.98

b. Jerry = 150, this means Tom would have been = 100 balloons/hr, difference in hours is less than 2
J = 150 * ~3.86 = 500 ( for this to exist, we have to ensure that it will give us a value of 500)

T = 100 * 5 = 500

c. Jerry = 180, this means Tom would have been = 120
here as well, when you compute the values, the difference in hours is less than 2

We can get the answer like this.
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Originally posted by KanishkM on 22 Jan 2019, 21:24.
Last edited by KanishkM on 27 Jan 2019, 21:40, edited 1 time in total.
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 27 Jan 2019, 21:16
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How do I do this using equations?
\(\frac{500}{x+2}=\frac{500}{x}\)
And J=1.5T

I went
\(\frac{500}{x+2}=\frac{500}{x}·\frac{1}{2}\) etc which I think is wrong (I got the wrong answer anyway)
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 27 Jan 2019, 22:00
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There is a formula for work done by two people

\(\frac{k_1*N_1*D_1*H_1*η}{W_1}\) = \(\frac{k_2*N_2*D_2*H_2*η}{W_2}\)

W = work done
N = no. of men
D = no. of days
H = no. of hours per day
Ƞ = Efficency
k = constant of prop

W = 500 by both Tom and Jerry
N = 1
H = x+2 for Tom and x for Jerry
Ƞ = 1.5 for Jerry and 1 for Tom

Using these info we get,

\(\frac{(x+2)*1}{500}\) = \(\frac{x*1.5}{500}\)

x+2 = 1.5x
0.5x = 2
x = 4
Jerry takes 4 hours, while Tom takes 6 hours.

Jerry in 1 hour can fill \(\frac{500}{4}\) = 125 balloons.

A is the answer.
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 28 Jan 2019, 00:20
Afc0892
I've searched for your formula here and google and can't find anything. Please post some links as it's pretty interesting.

Can you please show an example when the constant of proportionality is needed?
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 28 Jan 2019, 01:24
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philipssonicare, I found this formula in CAT (Indian version of GMAT). But, I couldn't find any problem where constant of proportionality is used.
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 28 Jan 2019, 11:21
J = Jerry's balloons/hr rate; J*2/3=Tom's balloons/hr rate

500/(J*2/3)=(500/J)+2=how many hours Tom needs for 500 balloons
solve for J:
500*3/2=500+2J
J=125
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom  [#permalink]

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New post 27 Feb 2019, 10:04
philipssonicare wrote:
How do I do this using equations?
\(\frac{500}{x+2}=\frac{500}{x}\)
And J=1.5T

I went
\(\frac{500}{x+2}=\frac{500}{x}·\frac{1}{2}\) etc which I think is wrong (I got the wrong answer anyway)

Considering time taken by Jerry as x and that by Tom as x+2 we have:
\(\frac{500}{x}=\frac{3}{2}(\frac{500}{x+2})\)
Solving the eqn gives x=4.
Hence, Jerry can fill 500/4 = 125 water balloons.
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Re: Tom and Jerry are filling up 500 water balloons a piece. It takes Tom   [#permalink] 27 Feb 2019, 10:04
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