SOLUTION: Two pumps can fill a water tank in 104 minutes when working together. Alone, the second pump takes 2 times as long as the first to fill the tank. How many minutes does it take the

Question 538094: Two pumps can fill a water tank in 104 minutes when working together. Alone, the second pump takes 2 times as long as the first to fill the tank. How many minutes does it take the first pump alone to fill the tank?

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
1/A = pump 1's rate of filling the tank per min.
1/B = pump 2's rate of filling the tank per min.
.
(1/A+1/B)*104 min = 1 filled tank = 1 whole job done
.
A can do the work twice as fast as B.
.
1/A = 2/B
.
substitute
.
(2/B + 1/B) * 104 = 1
.
3/B * 104 = 1
.
312/B = 1
.
cross multiply
.
312 = B
.
B can fill the tank in 312 min.
or
B does 1/312 of the job per min.
.
1/A = 2/312 = 1/156
or
A can do the job in 156 min.
.
Check by determine how much of the tank each can fill in 104 min.
1/312 * 104 = 104/312 = 1/3
1/156 * 104 = 104/156 = 2/3
1/3 + 2/3 = 1 filled tank
Correct.
.
Answer: The first pump can fill the tank in 156 minutes working alone.
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