SOLUTION: A new type of pump can drain a certain pool in 4 hours. An older pump can drain the pool in 6 hours. How long will it take both pumps working together to drain the pool?

Question 1135838: A new type of pump can drain a certain pool in 4
hours. An older pump can drain the pool in
6 hours. How long will it take both pumps working together to drain the pool?
Found 3 solutions by josmiceli, greenestamps, Alan3354:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Add their rates of pumping
Newer pump:
[ 1 pool drained ] / [ 4 hrs ]
Older pump:
[ 1 pool drained ] / [ 6 hrs ]
Working together:
[ 1 pool drained ] / [ t hrs ]
-----------------------------------

Multiply both sides by

2 hrs and 24 min

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Here is an alternative method for working these "working together" problems that you might like to try. Many students like this method because it avoids using fractions.

Consider the two pumps and several pools of the given size, and look at the least common multiple of the times it takes each of the two pumps.

The LCM of 4 and 6 is 12. In 12 hours, the new pump could fill 12/4 = 3 pools; in 12 hours, the old pump could fill 12/6 = 2 pools.

So in 12 hours the two pumps together could fill 3+2 = 5 pools; therefore the time required by the two together to fill one pool is one-fifth of 12 hours, or 12/5 hours.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A new type of pump can drain a certain pool in 4
hours. An older pump can drain the pool in
6 hours. How long will it take both pumps working together to drain the pool?
-----------------
There's a shortcut for problems like this:
4*6/(4+6) = 2.4 hours
=========================
Greenstamps' method is similar, but I wouldn't bother with the LCM, just use the product, 6*4 = 24. Same result.
Teachers and texts seem to be obsessed with LEAST common multiple, for no good reason. Just wastes your time.
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