Question

Joe can cut and split a cord of firewood in 6 fewer hours than Steve can. When they work​ together, it takes them 4 hours. How long would it take each of them to do the job​ alone?

Answer 1

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight =

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe =

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them =

⇒ Per hour rate of ( Dwight + Joe) =

Now, solving for the value of K , we get:

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.