how long will it take to fill the pool if only hose A is used?

Question

john has two garden hoses, A and B, to fill a pool, He estimates that hose A alone can fill the pool 1.5 times faster than hose B. working together, both hoses take 6 hours to fill the pool. how long will it take to fill the pool if only hose A is used?

Answer 1

This is a rate problem.

 

rate = number of pools/time

 

R_A = 1.5R_B

 

 

 

To fill one pool working together,

 

R_A + R_B = 1/6

 

1.5R_B + R_B = 2.5R_B = 1/6   [1]

 

 

 

 

To fill one pool with Hose A working alone,

 

R_A= 1/t

 

1.5R_B = 1/t  [2]

 

 

 

Use [1] and [2] to solve for t.

 

 

Ans:  10 hours.