Question

Al and Tom are painting a shed. Working alone, Al can paint the shed in 2 hrs. Together they can paint the shed in 1.5 hours. How long would it take Tom to paint the shed on his own?

Answer 1

6 hours.

Explanation:

The formula sort of has to be invented.

Al

rate = 1 shed / 2 hours

Tom

rate = 1 shed / x hours.

Together.

rate = 1 shed / 1.5 hours.

Equation

1 shed / 2 hours + 1 shed / x hours = 1 shed / 1.5 hours.

1/2 + 1/x = 1/1.5 Put the fractions over a common denominator.

(x + 2) / 2x = 1 / 1.5 Cross Multiply

1.5(x + 2) = 2x Remove the Brackets.

1.5x + 3 = 2x Subtract 1.5x from both sides

3 = 2x - 1.5x

3 = 0.5x Multiply both sides by 2

6 = x

It would take Al 6 hours to do the shed on his own.