Filling a tank with 2 taps

HOME

Math Central

Quandaries & Queries

Question from Murray, a parent:

My son has a question that I'm trying to help him with. It's a word problem and
we are having trouble formulating an equation that suits the question. If you could
give us a pointer or two, it would be appreciated. The question is:

2 taps turned on together can fill a tank in 15 minutes. By themselves, one
takes 16 minutes longer than the other to fill the tank.Find the time taken to
fill the tank by each tap on it's own.

I've tried letting the volume of the tank be equal to the two tap rates time
the time to fill the tank. V=(R1+R2)*15 and then letting each individual
time be T1=V/R1 and T2=V/R2. and then letting T1+16=T2 but it seems
to get overly complicated. Are we on the right track? Thanks.

Murray,

You aren't doing badly. If you solve T1 = V/R1 for R1 and T2 = V/R2 for R2 and then substitute
those into 15*(R1 + R2) = V, you will have an equation with variables T1 and T2. Substitute T2 = T1 + 16 to obtain an equation in the one variable T1 and solve for T1.

Good luck.
Victoria and Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.