2 drains drain a pool in 8 hours. One is 1.5 times faster. How long will it take for the faster one to drain the pool itself?

Question

i have no clue how to set up this problem in order to solve it need help

Answer 1

If a drain is 1 1/2(3/2) times faster than another, then it drains in 2/3 the time it takes the slower drain.

If one drain is 1 1/2 times faster, the other is 1 1/2 times slower.

For example if a slow drain takes 6 hours, then the faster drain takes (2/3)*6=4 hours.

In other words the slow drain takes 1 1/2 times the fast drain which is (1 1/2)*4=6 hours.

There are different ways to set up the problem.

One solution is the following...

x=# of hours it takes the fast drain

(1.5)x=# of hours it takes the slow drain

Together it takes 8 hours.

(1/x) is the rate per hour of the fast drain

(1/1.5x) is the rate of the slow drain

(1/x)(8)+(1/1.5x)(8)=1 (job finished)

(8/x)+(8/1.5x)=1

multiply both sides by 3x

(3x)(8/x)+(3x)(8/1.5x)=3x(1)

24+16=3x (the x's cancel and 3/1.5=2)

40=3x

x=40/3

x=13 1/3 hours for the fast drain

(1.5)(40/3)=20 hours for the slow drain