Answer :
Time taken by the smaller hose to fill the pool on its own = 75 minutes
Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes
Time taken by the larger hose to fill up the swimming pool = 50 minutes
Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.
In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.
In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.
It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.
Hence 1/30 = 1/x +1/50
⇒ 1/30 = (50+x)/50x
⇒ 30 = 50x/(50+x)
⇒ 30 (50 + x) = 50x
⇒ 1500 + 30x = 50x
⇒ 20x = 1500
⇒ x = 1500/20
⇒ x = 75 minutes.
Thus the smaller hose alone takes 75 minutes to fill up the pool.
The question is incomplete. Find the complete question below:
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?
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