Question

2. A swimming pool can be filled in 12 hours, using the large pipe alone and in 18 hours with the small pipe
alone.
a. If both pipes are used, how long will it take to fill the pool?

b. if the fire department is asked to help out by using its tank, which alone can fill the pool in 15 hours, how long will it take to fill the pool if all three water sources are used simultaneously?

c.at the end of the summer a drain is left open and the pool empties in 24 hours. If the pool attendant who is preparing the pool for opineng day forgets to plug the drain, can the pool be filled in one day? If so, how long will it take? If not, explain why not. ​

Answer 1

Given :  A swimming pool can be filled in 12 hours, using the large pipe alone and in 18 hours with the small pipe  alone.

To Find : both pipes are used, how long will it take to fill the pool?

Solution:

swimming pool can be filled in 12 hours, using the large pipe alone

=> large pipe can fill pool in 1 hr = 1/12

swimming pool can be filled in 18 hours, using the small pipe alone

=>small pipe can fill pool in 1 hr = 1/18

Both pipes together can fill pool in 1hr = 1/12 + 1/18

= ( 3 + 2)/36

= 5/36

Hence both pipe will fill the pool in 36/5  = 7.2 hrs

7 hrs 12 mins

One more pipe can fill in 1hr = 1/15

Total in 1hr =  5/36  + 1/15   =  (25 + 12)/180

= 37/180

= 180/37  hrs

4.86 hrs

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