Question

Janet can shovel snow from her driveway in 55 minutes. Bill can do the same job in 45 minutes. How long would it take Janet and bill to shovel the driveway if they worked together?

Answer 1

Answer:

It would take 24.75 minutes for them to shove the driveway if they worked together.

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/x

Janet's rate: 1/55

Bill's rate: 1/45.

So

Together rate = Janet's rate + Bill's rate

We have to find x

$\frac{1}{x} = \frac{1}{55}+\frac{1}{45}$

The least common multiple between 55 and 45 is 495. So

$\frac{1}{x} = \frac{\frac{495}{55} + \frac{495}{45}}{495}$

$\frac{1}{x} = \frac{9 + 11}{495}$

$\frac{1}{x} = \frac{20}{495}$

$20x = 495$

$x = \frac{495}{20}$

$x = 24.75$

It would take 24.75 minutes for them to shove the driveway if they worked together.