Question

Carla and Frank can each wash a car and clean the interior in 2 hours, but Missy needs 3 hours to do the work. If the three work together, how long will it take to clean 7 cars?

Answer 1

Remark

Start by figuring this out for 1 car. Worry about the 7 part when you find 1.

This problem is used quite frequently in physics. For example resistors in parallel use the same equation.

Formula

1/frank + 1/carla + 1/missy = 1/ time taken to do 1 mar.

Givens

Frank = 2 hours

Carla = 2 hours

Missy = 3 hours.

Substitute and Solve

1/2 + 1/2 + 1/3 = 1/Three_together.

3/6 + 3/6 + 2/6 = 1/Three_together.

8/6 = 1/Three_together. Cross multiply

8 * Three_Together = 6*1

8 * Three_Together = 6 Divide by 8

Three_Together = 6/8 = 3/4 = 0.75 hours. or 45 minutes for 1 car

Seven Cars

For 7 cars multiply 0.75 by 7

7 * 0.75 = 5.25 hours. <<<< Answer