Question

Shawna can paint a fence in 8 hours. Kevin can paint the same fence in 4 hours. How long will it take them working together? Show all work.

Answer 1

Answer: 2.66 hours

Step-by-step explanation:

Shawana can paint a fence in 8hours which means in one hour she can paint 1/8 of a fence.

Kevin can paint the same fence in 4 hours, so in one hour he can paint 1/4 of the fence.

Together in 1 hour they can paint 1/8 + 1/4 = 3/8

Total hours for painting is 3/8 or 2.66 hours

Answer 2

Hello!

The answer is:

The will paint the same fence at the same time in 2.67 hours.

Why?

From the statement we know that Shawna can paint a fence in 8 hours while Kevin can paint the same in 4 hours, and we are asked to calculate how long will it take them to paint the fence working together, so, calculating we have:

For Shawna, we have:

$ShawnaRate=\frac{FencePainted}{TimeToPaint}\\\\ShawnaRate=\frac{1fence}{8hours}$

For Kevin, we have:

$KevinRate=\frac{FencePainted}{TimeToPaint}\\\\KevinRate=\frac{1fence}{4hours}$

So, the combined work for both Shawna and Kevin will be:

$CombinedWorkRate=\frac{1fence}{8hours} +\frac{1fence}{4hours}\\\\CombinedWorkRate=\frac{4fence.hours+8fence.hours}{32hours^{2}}\\ \\CombinedWorkRate=\frac{12fence.hours}{32hours^{2}}\\\\CombinedWorkRate=\frac{12fence.hours}{32hours^{2}}=\frac{3fence}{8hours}$

Now, if the want to paint the same fence at the same time, we can calculate it by the following way:

$\frac{3fence}{8hours}=\frac{1fence}{x(hours)}\\\\x=1fence*\frac{8hours}{3fence}=2.67hours$

Hence, the will paint the same fence at the same time in 2.67 hours.

Have a nice day!