Question

A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 5 hours. Rhonda can paint the same room in 6 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.

Answer 1

Answer: 2.72 hours

Step-by-step explanation:

Let's call $t_1$ while it takes Wade to paint the room

Let's call $t_2$ while it takes Rhonda to paint the same room.

Then we know that:

$t_1 = 5\ hours\\t_2 = 6\ hours$.

Let's call it t as it takes Rhonda and Wade to paint the same room working together.

Now we use the following formula to calculate t.

$\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}$

$\frac{1}{t}=\frac{1}{5}+\frac{1}{6}$

$\frac{1}{t}=\frac{11}{30}$

$t=\frac{30}{11}$

$t=2.72\ hours$

If they work together they will be able to paint the room in 2.72 hours