How many days would it take?

Question

David can finish a job in 7 days. Coby can finish the same job in 5 days. After working together for 2 days, Coby leaves. How many days will it take David to complete the job ?

Answer 1

Let's assume they are replacing 35 windows (This is arbitrary.. any reasonable assumption will work!)

So, David replaces 35 windows in 7 days or 5 windows/day

and Coby replaces 35 windows in 5 days or 7 windows/day

After working together for 2 days, they complete 2 x 12 = 24 windows

That leaves 35-24 = 11 windows to do.

David then completes the job 11 windows/5 windows/day = 11/5 days

So, it takes David 2.2 more days to complete the job for a total of 4.2 days to do the whole job.

Answer 2

Sahara, in case you wonder how to solve this kind of problem without inventing a number of windows, I offer you the same insights as Mark, without the invention.

As Mark showed you, these “shared work” problems require that you distinguish Rates from Times, and recognize that they are basically reciprocal, because

Work = Rate * Time

and in this case you can consider that there is 1 job to do.

Since we are given these Times

Td = 7

Tc = 5

we can translate them as needed into Rates

Rd = 1/7

Rc =1/5

And then let X = time for David to finish after 2 days of cooperation.

There is 1 job to do, and since Work = Rate * Time,

1 = Rd*(2+x)+ Rc*2

Substitute the numbers into this equation and solve for x

1 = (1/7)*(2 + x) + (1/5)*2

1 = (2 +x)/7 + 2/5

3/5 = 2/7 + x/7

21/5 - 2 = x

21 - 10= 5x

11 = 5x

X = 2.2