Question

It would take 1 person 70 days of work to

build a house extension.
2 people have been working for 7 days on
this house extension.
a) How many days would it have taken 1
person to do this amount of work?
b) How many days would it take 1 person to
finish building this house extension?

Answer 1

a) It would have taken 1 person 14 days to do this amount of work.

b) It would take 1 person 56 days to finish building this house extension.

We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.

Explanation:

Answer 2

To solve this problem, we can use the formula:

Work = Rate × Time

where "Work" is the amount of work done, "Rate" is the rate of work, and "Time" is the time it takes to do the work.

a) Let's assume that one person can do the job in "x" days. Therefore, the rate of work for one person is:

Rate for one person = 1/x

The total amount of work that two people can do in 7 days is:

Work = Rate × Time
Work = (1/x + 1/x) × 7
Work = 2/x × 7
Work = 14/x

We know that it would take one person 70 days to do the entire job. Therefore, the amount of work that one person can do in 7 days is:

Work = Rate × Time
Work = 1/70 × 7
Work = 1/10

Now we can equate the two amounts of work and solve for "x":

14/x = 1/10
x = 140

Therefore, one person would take 140 days to do the same amount of work that two people did in 7 days.

b) We can use the same formula, Work = Rate × Time, and plug in the rate of work for one person (1/x) and the total amount of work that needs to be done (1). Solving for "Time", we get:

Work = Rate × Time
1 = 1/x × Time
Time = x

Substituting x with 140, we get:

Time = 140

Therefore, it would take one person 140 days to finish building this house extension.