Solve Inverse Proportion Road Works in 14 Days

[LiHJ]

Homework Statement

Dear Mentors and PF helpers,

Please help me with this question as my junior asked me but I have some doubts in it:

It takes 4 workers to complete repairing the road in 42 days. Suppose that 14 days into the road works, 10 more workers are brought into help out in the road works. Calculate the total number of days needed to complete the road works in this case.

Homework Equations

y = k/x , where k is a constant and y and x are variables [/B]

The Attempt at a Solution

let y be days and x be number of workers
42 = k / 4
168 = k

From the question they trying to ask if during the 14 days of work with 14 men but after this 14 days it's going to be 4 men working again.

Suppose there are 14 workers ("10 more workers are brought into help..."):

d = 168 / 14 = 12

It takes 12 days to complete the repairing, but why the question says " Suppose that 14 days into the road works ..."

Can anyone help me? Thank you for your time.

 

[Stephen Tashi]

From the question they trying to ask if during the 14 days of work with 14 men but after this 14 days it's going to be 4 men working again.

No. I think there are 14 days of work by 4 men. Then 14 men work to finish the road.


First find the rate R at which 1 worker works. Use the fact that 4 men working at that rate can finish 1 road in 42 days.

(4 workers) (R) (42 days ) = 1 road

Solve for R

Then write the equation that says 14 men working at rate R for X days build 1-(4)(R)(14) of the road.

 

[Mark44]

Homework Statement

Dear Mentors and PF helpers,

Please help me with this question as my junior asked me but I have some doubts in it:

It takes 4 workers to complete repairing the road in 42 days. Suppose that 14 days into the road works, 10 more workers are brought into help out in the road works. Calculate the total number of days needed to complete the road works in this case.

Homework Equations

y = k/x , where k is a constant and y and x are variables [/B]

The Attempt at a Solution

let y be days and x be number of workers
42 = k / 4
168 = k

And what does k represent?

From the question they trying to ask if during the 14 days of work with 14 men but after this 14 days it's going to be 4 men working again.

Suppose there are 14 workers ("10 more workers are brought into help..."):

d = 168 / 14 = 12

It takes 12 days to complete the repairing, but why the question says " Suppose that 14 days into the road works ..."

Can anyone help me? Thank you for your time.

Your approach needs to be more systematic, taking into account that for the first 14 days only 4 men are working on the road, and then after that, an additional 10 men are working on it. What fraction of the job can the first four men do in the first 14 days? From this, what fraction of the job can each man do per day, assuming that all four men work at the same rate? How much of the job is left after the first 14 days? How long will it take for all of the men (all 14 of them) to finish the job?

 

[LiHJ]

Thank you Stephen and Mr Mark.

Here's my working:

If the job is to be done by 1 day, it will need 42 x 4 = 168 workers.
So first is being done by 4 men in 14 days, so is like 56 workers already did their part.
Left over work is 168 - 56 = 112 workers still needed to complete it.
Number of days left = 112/ 14 = 8 days
So total number of days required = 14+8 = 22 days

 

[Stephen Tashi]

I agree, except that I would change the words slightly. The unit of labor is "worker days" (similar to the idea of "man hours").

If 1 road is built by 4 men in 42 days, it will need 42 x 4 = 168 worker days.
The first phase is being done by 4 men in 14 days, they accomplish 56 worker days..
Left over work is 168 - 56 = 112 worker days still needed to complete it.
Number of days left to finish the job = 112/ 14 = 8 days
So total number of days required = 14+8 = 22 days