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WORD PROBLEM, BET U CANT DO IT

WORD PROBLEM, BET U CANT DO IT

Two taps turned on together can fill a tank in 15 minutes. By themselves, one takes 15 minutes longer than the other to fill the tank. find the time taken to fill the tank by each tap alone.
2 REPLIES 2

WORD PROBLEM, BET U CANT DO IT

The faster takes 7.5x(1+sqrt(5)), about 24 min 16.23 seconds. The slower, quite obviously, takes 15 minutes more than that.

If you would like to present a challenge, it may be more appropriate in the "StudyWorks Challenge" section at the bottom.

If you would like a few more details of the solution, you can suggest some things you have tried and we will be glad to clarify whatever you like.

WORD PROBLEM, BET U CANT DO IT

On 10/2/00 5:21:24 PM, Stormkill wrote:
>Two taps turned on together
>can fill a tank in 15 minutes.
>By themselves, one takes 15
>minutes longer than the other
>to fill the tank. find the
>time taken to fill the tank by
>each tap alone.

Let A be the fraction of the tank filled by the first tap. Let B be the fraction filled by the second tap. Thus, A+B represents the entire take, so it is 1. A+B=1.

Let t represent the time taken to fill the tank together. In this case, t=15 since we want t to be the time taken to fill the tank together. Let R and S be the rates at which both takes are filled.

Rt=A St=B A+B=1

Those are the equations I have so far. R is the rate at which it is filled. ie, rate = (fraction of tank) / (time to fill it). since the rate is calculated by the time taken to fill the tank, rate = 1 / time. Let T and U be the times required for each tap to fill it alone.

R=1/T S=1/U

Rt+St=1 combine the first set of equations

t/T+t/U=1 or 1/T+1/U=1/t

The formula is well known and is easily generalized. if n taps working together can perform the task in t1, t2, t3, ..., tn time, the time taken if they work together is

1/t=1/t1+1/t2+1/t3+...+1/tn.

This formula applies in many occasions. (eg, people mowing lawns)

Back to your problem.

Because one tap is 15 minutes faster, let U=T+15. Of course, t=15.

1/T+1/(T+15)=1/15

multiply both sides by the denominators to remove the fractions.

15(T+15)+15T=T(T+15)

15T+225+15T=T^2+15T

225+15T=T^2

T^2-15T-225=0

Solve this and the results is as Nathan said.

Craig
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