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

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) (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

.
If tap #2 can fill the bath in 5 hours when there is no leak,
it delivers water at a rate of

.
If tap #3 can fill the bath in 10 hours when there is no leak,
it delivers water at a rate of

.

All three taps together can deliver water at a rate of

.
With a leak the water level will increase at a rate of
.

1) At that rate the pool will fill in
.

2) Over that time, the 3 taps will have delivered
.
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