GMAT prep PS question

[mlane25269]

Can someone explain? Thanks!

[Pedros]

is the OA 12 ?

[Pedros]

The first hose does 1/20 of the work per hour
The second hose does 1/30 of the work per hour

combining them together; 1/20 + 1/30 = 5/60 = 1/12 per hour

they together finish 1/12 of the work per hour
so 100% of the work will be done in 12 hours. ( cross multiply)

another way to think about it :
Hose 1 finish in 20 hours
Hose 2 finish in 30 hours

so they finish 2 pools in 50 hours
Therefore they finish one pool in 25 hours average if they work independatly. If they work simultinously it would take them together halh that time. which is 12.5 hours ( approximatly )

so i think its 12 not 10.

[Ian Stewart]

another way to think about it :
Hose 1 finish in 20 hours
Hose 2 finish in 30 hours

so they finish 2 pools in 50 hours
Therefore they finish one pool in 25 hours average if they work independatly. If they work simultinously it would take them together halh that time. which is 12.5 hours ( approximatly )

Your first answer was correct, but the above is not, as you might be able to tell; it gives you a different answer from your first solution, so one of them must be incorrect, of course. You can't average combined rates in the way you've done above.

There is another way to look at the problem:

- If A fills the pool in 20 minutes, two hoses just like A would take 20/2 = 10 minutes. We don't have two hoses like A; we have one like A, and one slower than A, so it must take more than 10 minutes for A+B together.

- If B fills the pool in 30 minutes, two hoses just like B would take 30/2 = 15 minutes. We don't have two hoses just like B; we have one like B, and one faster than B, so the time for A+B together must be less than 15 minutes.

So the answer must be between 10 and 15, and 12 is the only possibility among the answer choices.

[lilu]

Large hose's rate=1/20
Small's rate=1/30
Add rates together because they need to be working together=1/20+1/30=5/60
Now time=work/rate=1/(5/60)=60/5=12