Question

Two pipe working together takes 28 4/7 minutes to fill a tank. If pipe takes 60 minutes less than pipe b.

Answer 1

Answer:

Pipe A = 40 mins

Pipe B = 100 mins

Step-by-step explanation:

Define x:

Let Pipe A takes x mins

Pipe B takes (x + 60) mins

Find the work done by Pipe A in 1 min:

1 min = 1/x of the work

Find the work done by Pipe B in 1 min:

1 min = 1/(x + 60) of the work

Find the work done by Pipe A and B in 1 min:

1 min = 1/x + 1/(x + 60)

1 min = (x + 60 +x) / x(x + 60)

1 min = (2x + 60) / (x² + 60x)

Find the work done by Pipe A and B in 1 min:

The two pipes take 28 4/7 min = 200/7 min

1 min = 7/200 of the work

Solve x:

(2x + 60) / (x² + 60x) = 7/200

200(2x + 60) = 7(x² + 60x)

400x + 12000 = 7x² + 420x

7x² + 20x - 12000 = 0

(x - 40) (7x + 300) = 0

x = 40 or x = - 300/7 (rejected, since x cannot be negative)

Find the time each pipe takes:

Pipe A = x = 40 mins

Pipe B = (x + 60) = 40 + 60 = 100 mins

Answer: Pipe A takes 40 mins and Pipe B takes 100 mins