It takes 12 hours to fill a pool with the inlet pipe. It can be emptied in 15 ho

Question

It takes 12 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the outlet pipe. If the pool is 2/3 full to begin with, how long will it take to fill it from there if both pipes are open?

Time: ____hours

In exercise physiology, a person's maximum heart rate, in beats per minute, is found by subtracting his age in years from 220. So, if A represents your age in years, then your maximum heart rate is:

M=220AM=220-A

A: Use this formula to find the maximum heart rate for a person who is 30 years old.

Maximum heart rate: beats per minute

A person's training heart rate, in beats per minute, is his resting heart rate plus 60% of the difference between his maximum heart rate and his resting heart rate. If resting heart rate is R and maximum heart rate is M, then the formula that gives training heart rate is:

T=R+0.6(MR)T=R+0.6(M-R)

B: Use this formula along with your result from above to fill in the following table for a person 30 years old.

Resting Heart Rate
(beats per minute) Training Heart Rate
(beats per minute) 70 72 74 76 78

Explanation / Answer

It takes 12 hours to fill a pool with the inlet pipe.

Time taken to full 2/3 full = 12*(2/3)

= 8 hours

so,

8 hrs to fill 2/3 the pool:

so,rate = 1/8 hrs/ 2/3 full pool

It can be emptied in 15 hours with the outlet pipe.

so, (15*(2/3)) hrs

= 10 hrs to empty 2/3 the pool

hence,rate = (1/10) hrs/ 2/3 -pool

Working together let rate = x hrs/ 2/3 -pool

so,

Equation will be :

1/8 - 1/10 = 1/x

1/40 = 1/x

1/x = 1/40

hence, x = 40

so, x = 40 hrs (time to fill 2/3 of the pool)                    [ Answer ]

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