2 different sized hoses

Question

Working together, it takes two different sized hoses 30

minutes to fill a small swimming pool. If it takes 50

minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

Answer 1

The larger hose can fill the pool in 50 minutes........so in 1 minute, it can fill 1/50 th of the pool.

The smaller hose can fill the pool in s minutes........so in 1 minute, it can fill 1/s of the pool.

 

Together they can fill 1/50 + 1/s........or (S+50)/50s.

 

But together, it takes 30 minutes, while our expressions is how much of the job can be done in 1 minute....so in 1 minute, they complete 1/30 th of the job.

 

So (s+50)/50s = 1/30      cross multiply

30s + 1500 = 50s

          1500 = 20s

              75 = s

 

So the smaller hose can fill the pool in 75 minutes by itself.

 

Hope this helped.