SOLUTION: A bath has a capacity of 150 liters. Oddly it has 3 taps. The first can fill the bath in 3 hours, the second in 5 hours and the third in 10 hours. Knowing the bath is leaking 35

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A bath has a capacity of 150 liters. Oddly it has 3 taps. The first can fill the bath in 3 hours, the second in 5 hours and the third in 10 hours. Knowing the bath is leaking 35      Log On


   

Question 814628: A bath has a capacity of 150 liters. Oddly it has 3 taps. The first can fill the bath in 3 hours, the second in 5 hours and the third in 10 hours.
Knowing the bath is leaking 35 liters per hour:
1) How long does it take, despite the leak, using all 3 taps simultaneously?
2) How much water is consumed?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If tap #1 can fill the bath in 3 hours when there is no leak,
it delivers water at a rate of
150L%2F%223+hr%22=+50%22L+%2F+hr%22 .
If tap #2 can fill the bath in 5 hours when there is no leak,
it delivers water at a rate of
150L%2F%225+hr%22=+30%22L+%2F+hr%22 .
If tap #3 can fill the bath in 10 hours when there is no leak,
it delivers water at a rate of
150L%2F%2210+hr%22=+15%22L+%2F+hr%22 .

All three taps together can deliver water at a rate of
50%2B30%2B15=95%22L+%2F+hr%22 .
With a 35%22L+%2F+hr%22 leak the water level will increase at a rate of
95-35=60%29%29%29%7B%7B%7B%22L+%2F+hr%22 .

1) At that rate the pool will fill in
150L%2F%2260+L+%2F+hr%22=highlight%282.5hours%29 .

2) Over that time, the 3 taps will have delivered
%282.5hr%29%28%2295+L+%2F+hr%22%29=highlight%28237.5L%29 .