Question

A tank fitted with two pipes is to be filled with water. The first pipe can fill it in 10 hours. After it has been open for 5 hours, the second pipe is opened and the tank is filled in 2 hours more. How long will it take the second pipe to fill the tank alone?

Answer 1

After 5 hours, the tank is half full, so
1/10 + 1/x = (1/2)/2
x = 20/3 hr

check:
pipe 1 can fill 1/10 of the tank per hour
pipe 2 can fill 3/20 of the tank per hour
5/10 + 2(1/10 + 3/20) = 5/10 + 10/20 = 1

Answer 2

(1/10)(5)+(2)[(1/10)+(1/x)] = 1
x = 20/3 hrs