Question

Henry can wash a car in 35 minutes, and Robert can wash in 14 minutes.How long would it take them to wash the car working together? Set up the problem algebraically and solve. State what your variable represents.

Answer 1

Henry and Robert will take 10 minutes to wash the car together. You find this by adding their work rates together (1/35 + 1/14) and then finding the reciprocal to get the time it takes both working together.

Step-by-step explanation:

To find out how long it will take for Henry and Robert to wash a car working together, we can set this up algebraically. Let's let x represent the amount of time it takes for both of them to wash the car together.

Firstly, we need to know how much of the car they can wash individually in one minute:

Working together, each minute they will wash:

1/35 + 1/14 of a car.

Simplifying this, we get:

1/35 + 1/14 = 2/70 + 5/70 = 7/70 of a car in one minute.

The time it takes for both of them to wash the whole car working together is thus:

1 / (7/70) = 70/7 minutes.

When we calculate this, we find that:

70/7 = 10 minutes.

So, it would take Henry and Robert 10 minutes to wash the car working together.