Question

Suppose that a small pump can empty a swimming pool in 70 hours and that a large pump can empty a pool in 30. Working together, how long will it take to empty the pool?

Answer 1

for small pump, in 1 hr, it empties 1/70 of the pool..
for large pump,in 1 hr, it empties 1/30 of the pool..
together, for t hrs, they empty t/70 and t/30 of the pool each,
thus our required eqn would be
(t/70) + (t/30) =1

hope this helps..

Answer 2

in these type of question first of all we must find out in unit time what part of the work isdone
thus in 1 hr fisrt pump can empty 1/70 part of swimming pool
in 1 hr fisrt pump can empty 1/30 part of swimming pool
when together
in 1 hr they can empty (1/70+1/30) =3+7/210 =1/21
thus they can empty 1/21 of swimming pool in 1 hr
hence the reqd time is 1/(1/21)=21 hr

Answer 3

So let's see, we know that they're both emptying 1 pool in an amount of time, but this doesn't help us since we need to know their rates of emptying pools.

One Pool Emptied=(Rate of Pool Emptying) x (hours of emptying)

So we can see that we know the hours of emptying is 70 and 30 and they're both emptying 1 pool so we can write it as:

1=r*70
and the other as
1=R*30

and solve for their rates.

See, if you know their rates, that'll tell you how much of the pool they drain per hour. Then we can add their rates together.

Think of it like this. If I can eat 5 cookies in an hour and my friend eats 7 cookies in an hour, how many do we eat per hour if we're both eating cookies? 12 cookies per hour, right? So from there we can add our rates together and then solve for the amount of time it takes to empty 1 pool again

1=(R+r)*T

And from there you can solve for time!