# algebra

Pump A can fill a swimming pool in 6 hours and pump B can fill the same pool in 4 hours. The two pumps began working together to fill an empty pool, but after 40 minutes pump B broke down, and pump A had to complete the job alone. The pool was scheduled to open 4 hours after the pumping started. Was it full by then, or did the opening have to be delayed?

1. 👍 0
2. 👎 0
3. 👁 596
1. rewording to indicate the rate of completion,

a = 1/6 pool/hr
b = 1/4 pool/hr

they work together for 2/3 hour, so they filled

(1/6 + 1/4)*2/3 = 5/18 pool

So, how long does it take A to fill the other 13/18 pool?

13/18 / 1/6 = 13/3 hour

So, the whole pool took 2/3 + 13/3 = 15/3 = 5 hours to fill, finishing an hour late.

1. 👍 0
2. 👎 0
2. T = t1*t2/(t1+t2) = 6*4/(6+4) = 2.4h = 144 Min. to fill the tank.

40min./144min. * 1 = 5/18 of a tank in 40 min.

1-5/18 = 18/18 - 5/18 = 13/18 to be filled by pump A.

13/18 * 6h = 4 1/3h = Time required for pump A to finish the job. But this is greater than the 4-hour limit to do the job. So the opening had to be delayed.

4 1/3 + 40/60 = 13/3 + 2/3 = 5h = Tot.
to do the job.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### statistics

A service station has a pump that distributes diesel fuel to automobiles. The station owner estimates that only about 3.2 cars use the diesel pump every 2 hours. Assume the arrivals of diesel pump users are Poisson distributed. a.

2. ### calculus

A circular swimming pool has a diameter of 14 m, the sides are 4 m high, and the depth of the water is 3.5 m. (The acceleration due to gravity is 9.8 and the density of water is 1000 .) How much work (in Joules) is required to:

3. ### physics - another thermo problem

A bicycle pump is a cylinder 20 cm long and 3.0 cm in diameter. The pump contains air at 25.0 C and 1.0 atm. If the outlet at the base of the pump is blocked and the handle is pushed in very quickly, compressing the air to half

4. ### math

Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 2 hours. The larger pipe can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an

1. ### c

A hose can fill a swimming pool in 4 hours. Another hose needs 9 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

2. ### Physics

2. A pool has an area A = 50 m2 and depth h = 2.5 m. The pool is filled with water to the maximum height. An electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a

3. ### math

Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened

4. ### math

One pipe can fill a swimming pool in 8 hours. Another pipe takes 12 hours. How long will it take to fill the pool if both pipes are used simultaneously?

1. ### math

One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 7 days. How long will it take the two pumps, working together, to empty the pool?

2. ### Math

It takes an older pump 4 times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 4 hours to drain the pool. How long will it take the older pump to drain the pool working alone?

3. ### math

One pipe can fill a pool in 10 hours. Another pipe can fill the pool in 30 hours. How long would it take them to fill the pool if they were working together?

4. ### Algebra

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?