Problema Solution
Two pipes are connected to the same tank. When working together, they can fill the tank in 4 hours. The larger pipe, working alone, can fill the tank in 6 hours less time than the smaller one. How long would the smaller one take, working alone,to fill the tank?
Answer provided by our tutors
Let x = time (hours) it takes for smaller one alone
then
x-6 = time (hours) it takes for larger one alone
.
4(1/x + 1/(x-6)) = 1
multiplying both sides by x(x-6):
4((x-6) + x) = x(x-6)
4(2x-6) = x^2-6x
8x-24 = x^2-6x
-24 = x^2-14x
0 = x^2-14x+24
0 = (x-2)(x-12)
x = {2,12}
throw out the 2 (extraneous) because it doesn't make sense leaving:
x = 12 hours