It took 3 people 2 1/2 hours to paint a large room. How long would it take 5 people to paint a similar room? Write the expression represented by this problem and then show all of your steps to arrive at the final answer.

Answer: it will take 5 people 1.5 hours

Step-by-step explanation:

It took 3 people 2 1/2 hours to paint a large room. Changing from mixed fraction to improper fraction, 2 1/2 hours will be 5/2 hours. Therefore,

It took 3 people 5/2 hours to paint a large room.

For 5 people to paint a similar room, it will take them lesser time. Thi s is an inverse variation. Therefore, the number of people is varies inversely

with the time it takes them to paint the room.

Let number of people be p and time it takes be t

p varies inversely with t.

Introducing constant of variation, k, it becomes

p = k/t

If 3 people take 5/2 hours, then

3 = k / (5/2)

k = 3 * 5/2 = 7.5

Our expression becomes

p = 7.5/t

The time it will take 5 people will be

p = 5 so,

5 = 7.5/t

t = 7.5/5 = 1.5 hours