Answer: it will take 5 people 1.5 hours
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