Joe can cut firewood in 9 fewer hours than Dwight can. When they work together it takes them 6 hours. How long would it take each of them to do the job alone?

Question

it would take joe _ hours

it would take dwight _hours

Answer 1

Let's look at rates.

 

Assume that Dwight can cut 1 firewood in 'd' hours. then that means that Joe can cut 1 firewood in d - 9 hours, since he cuts the firewood in 9 fewer hours than Dwight.

 

Now imagine that they are cutting 1 firewood, where Dwight starts cutting at one end and Joe starts cutting from another end. Won't it be pretty clever to assume that the new rate that they cut the firewood will be the sum of their individual rates?

 

For example, if Dwight can cut ^{1 firewood}/_{d hours}, then Joe can cut ^{1 firewood}/_{d - 9 hours} and we can assume that they can cut ^{1 firewood}/_{d hours} + ^{1 firewood}/_{d - 9 hours}

 

Now the combined rate is ^{1 firewood}/_{6 hours}, so we have ^{1 firewood}/_{d hours} + ^{1 firewood}/_{d - 9 hours} = ^{1 firewood}/_{6 hours}

 

But we know how to do algebra, don't we :)

 

Tutors, please feel free to review my explanation.