Elam can wire a light in 40 minutes. Michael can wire a
light in 60 minutes. How long
would it take them to wire the
light together?

24 minutes

Step-by-step explanation:

We use 1/a + 1/b = 1/c

where a and b are the individual times and c is the time together

1/40 + 1/60 = 1/c

Multiply each side by 120c

120c( 1/40 + 1/60 = 1/c)

3c + 2c = 120

5c = 120

Divide each side by 5

5c/5 = 120/5

c = 24

24 minutes

Step-by-step explanation: To solve this kind of a problem which is called a work problem, it's important to understand the following idea.

Since Elam can wire a light in 40 minutes, we know that in 1 minute,

Elam can wire 1/40 of the light and in 2 minutes, Elam can wire 2/40 of it.

Therefore, in t hours, Elam can wire t/40 of the light.

The same applies for Michael, in t hours, he can wire t/60 of the light.

So to solve the problem, we use the following formula:

Part of job done by Elam + part of job done Michael = 1 job done

The part of the job done by Elam is t/40 and t/60 for Michael.

So we have t/40 + t/60 = 1.

Now multiply both sides by 120 to get 3t + 2t = 120

or 5t = 120 so t = 24.

So it takes 24 minutes if they work together.