one pump can empty a pool in 5 days, wheras a second pump can emtpy pool in 7 days. how long will it take the two pumps, working together, to empty the pool?
rate of 1st pump = pool/5
rate of 2nd pump = pool/7
combined rate =pool/5 + pool/7 = 12 pool/35
time at combined time = pool/(12pool/35)
= 35/12 = 2.91666.. days
To find out how long it would take the two pumps, working together, to empty the pool, we need to calculate their combined rate of work.
Let's denote the rate of work of the first pump as "P1" (which empties the pool in 5 days) and the rate of work of the second pump as "P2" (which empties the pool in 7 days).
The rate of work is inversely proportional to the time taken. So, the rate of work for each pump can be calculated as:
P1 = 1 pool / 5 days = 1/5 pools per day,
P2 = 1 pool / 7 days = 1/7 pools per day.
When two pumps work together, their rates of work add up. So, the combined rate of work, denoted as "P_total", can be calculated as the sum of their individual rates:
P_total = P1 + P2.
Substituting the values we have:
P_total = 1/5 + 1/7.
To simplify this expression, we need to find a common denominator:
P_total = 7/35 + 5/35.
Now, we can add the fractions:
P_total = 12/35 pools per day.
Hence, the two pumps, working together, can empty 12/35 of the pool in one day. To find out how many days it will take to empty the entire pool, we can calculate the reciprocal of the combined rate:
Time = 1 / P_total = 1 / (12/35) = 35/12.
Therefore, it would take approximately 2.92 (35/12) days for the two pumps, working together, to empty the entire pool.