Question

There are two groups of people, three in each, for painting a wall. The numbers in the next two sentences express the time (in hours) spent on painting. In group A, Alex 2.5, Adam 3.6, and Antimo 4.7. In group Z, Zairo 2.2, Zeno 3.2, and Zubro 4.9. Estimate the total time for group A and for group Z when all three workers in each group work together. Which group can paint the wall faster and why do you think so?

(your answer is two numbers
(two estimates) in one sentence where you will explain your reasoning)​

Answer 1

1. The total time taken for group A to paint the wall together is 1.12 hours

2. The total time taken for group Z to paint the wall together is 1.03 hours

3. group Z can paint the wall faster

Explanation:

The time spent on painting are;

Group A

Alex = 2.5 hours

Adam = 3.6 hours

Antimo = 4.7 hours

1. We have for group A

Alex's paint rate = 1 wall in 2.5 hours = 1/2.5 wall/hour

Adam's paint rate = 1 wall in 3.6 hours = 1/3.6 wall/hour

Antimo's paint rate = 1 wall in 4.7 hours = 1/4.7 wall/hour

When the three workers work together, we have;

1/2.5 wall/hour + 1/3.6 wall/hour + 1/4.7 wall/hour = 3767/4230 wall/hour

Therefore, the time for the three workers of group A to paint one wall is given as follows;

`Time \ to \ paint \, one \, wall = (1 \, wall)/((3767)/(4230) wall/hour) = 1\tfrac{463}{3767} hours`

The total time taken for group A to paint the wall together = 1.12 hours

2. The data for group Z is as follows;

Zairo = 2.2 hours

Zeno = 3.2 hours

Zubro = 4.9 hours

We have for group Z

Zairo's paint rate = 1 wall in 2.2 hours = 1/2.2 wall/hour

Zeno's paint rate = 1 wall in 3.2 hours = 1/3.2 wall/hour

Zubro's paint rate = 1 wall in 4.9 hours = 1/4.9 wall/hour

When the three workers work together, we have;

1/2.2 wall/hour + 1/3.2 wall/hour + 1/4.9 wall/hour = 8375/8624 wall/hour

Therefore, the time for the three workers of group Z to paint one wall is given as follows;

`Time \ to \ paint \, one \, wall = (1 \, wall)/((8375)/(8624) wall/hour) = 1\tfrac{249}{8375} hours`

The total time taken for group Z to paint the wall together = 1.03 hours

3. Since the total time for group A to paint the wall which is 1.2 hours is more than the total time for group Z to paint the wall which is 1.03 hours, group Z can paint the wall faster.