SOLUTION: Beth could do P problems in 2 hours and Mollie could do X problems in H hours. How long would they have to work together to finish 400 problems?

Question 1092780: Beth could do P problems in 2 hours and Mollie could do X problems in H hours. How long would they have to work together to finish 400 problems?
Found 2 solutions by jorel1380, Gentle Phill:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
If Beth can do P problems in 2 hours, and Mollie can do X problems in H hours, then, together they can do:
P/2 + X/H problems per hour, or PH+2X. So, to do 400 problems, they would need:
400/(PH+2X) hours
☺☺☺☺
Answer by Gentle Phill(18) (Show Source): You can put this solution on YOUR website!
Let's put it to note that:
Ability = No. of Problems/Time taken
.
Thus, let:
Beth's ability = B
Mollie's ability = M
.
B = P/2hrs ... 1
M = X/Hhrs ... 2
.
(B+M) = 400/T
.
Where T = time needed to finish problems.
.
Substitute B and M with values from eqn 1 and 2
.
[(P/2hrs)+(X/Hhrs)] = 400/T
.
Make T subject of the relation.
.
(HP+2X)/2Hhrs = 400/T
.
T(HP+2X) = 2H(400)hrs
.
T = [800H/(HP+2X)]hrs
.
.
.
Your friend,
Francis.
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