Thread: Basic Work Problem

I think I might be over thinking this.

It takes a crew of eight construction workers working whole days a total of 42 days to complete a highway project. How many days will it take to complete the highway project if one construction worker (out of the crew of eight) starts working half days?

The "whole day" and "half day" in the problem do not mean a literal 24 hour or 12 hour period. I've tried to solve by using "x" to represent a half day. Thus, before the guy starts working half days, the entire crew works 16 half-days each day. After the guy starts working half days, the entire crew works 15 half-days each day. I don't seem to be making any progress though.

Any help would be appreciated.

I think I might have solved this.

Work = Rate x Time

1 job = 8 Rate (because 8 people) x 42 days

Solving for the rate: R = 1/336

Therefore, the new equation taking into consideration that one worker is now work half days:

1 job = 7.5 rate x Time
1 job = 7.5 (1/336) x Time

Solving for time, it is 44.8 days. Is this the correct way to solve it?

Thanks in advance!