Answer:
How long will it take 6 people to wash all the cars? 5 hours 20 minutes
If you only have 2 hours and 40 minutes to wash all the cars how many people will you need? 12 people
Explanation:
The important thing to realize here is that the time taken to wash x cars is inversely proportional to the number of people
That is represented mathematically as
y ∝ 1/x
The more the number of people, the less time it takes
We can write this as a proportionality equation:
y = k/x
where k is referred to as the constant of proportionality
We have the information: 4 people take 8 hours.
Plugging these two values into the equation
4 = k/8
k = 4 x 8 = 32 hours
So it takes 1 person 32 hours to wash all the cars
If there were 6 people instead
6 = 32/h where h is the time taken for 6 people to wash 30 cars
h = 32/6 = 16/3 hours = 5 1/3 hours
= 5 hours and 20 minutes
2 hours and 40 minutes = 2 40/60 hours = 2 2/3 hours
Converting to improper fraction
2 2/3 = (2 x 3 + 2)/3 = 8/3 hours
Plugging this value of x into the equation gives
y = 32/(8/3)
32 ÷ 8/3 is computed by flipping the fraction and multiplying
32 ÷ 8/3 = 32 x 3/8 = 12 people