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?
Pump 1 does (1/5) pool/day
pump 2 does (1/7) pool/day
together they do (1/5)+(1/7) pool/day
that is
7/35 + 5/35 = 12/35 pool/day
so it will take 35/12 = 2.92 days/pool
thank you both
I'm glad you asked! Well, when it comes to teamwork, these pumps sure know how to make a splash! So, let's get to work-solving this watery puzzle.
If the first pump alone can empty the pool in 5 days, that means in one day, it can drain 1/5th of the pool. Similarly, the second pump can drain 1/7th of the pool in one day.
Now, when the two pumps work together, their combined pump power can drain a grand total of 1/5 + 1/7 (or should I say 12/60 + 15/60) of the pool in one day. When we add those fractions together, we get 27/60, or 9/20.
So, working as a dynamic duo, these pumps can drain 9/20 of the pool in one day.
To find out how long it will take for them to empty the entire pool, we need to flip their combined draining power fraction. That gives us 20/9. So, it will take approximately 20/9 days (or about 2 and a quarter days) for these spectacular pumps to high-five each other and successfully empty the pool!
To find out how long it will take the two pumps, working together, to empty the pool, we need to calculate their combined rate of emptying the pool.
Let's first find the individual rates of each pump. The first pump can empty the pool in 5 days, so it can empty 1/5th of the pool in one day. Similarly, the second pump can empty 1/7th of the pool in one day.
To find their combined rate, we add their individual rates. So the combined rate is 1/5 + 1/7 = (7 + 5)/35 = 12/35.
Now that we know the combined rate of the pumps, we can find out how long it will take them to empty the pool by dividing the total pool capacity by their combined rate.
Let's assume the pool capacity is 1 unit (you can assume any unit as long as it's consistent). So, to empty 1 unit of the pool, it will take 35/12 days, which is approximately 2.92 days.
Therefore, it will take the two pumps, working together, approximately 2.92 days to empty the pool.
rate of 1st pump = pool/5
rate of 2nd pump = poo/7
combined rate = pool/5 + pool/7 = (12/35)pool
time at combined rate = pool / ((12/35)pool) = 35/12 or 2.916667
it will take about 2.92 hours or 2hrs, 55 minutes