Respuesta :
Answer:
Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.
Step-by-step explanation:
Let us assume the time taken by Dwight to split a cord of firewood = K hrs
So, the per hour rate of Dwight = [tex](\frac{1}{K})[/tex]
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 = [tex](\frac{1}{K-3})[/tex]
Now, when both of them wok together, it takes them 2 hours.
So, the per hour rate of BOTH of them = [tex](\frac{1}{2})[/tex]
⇒ Per hour rate of ( Dwight + Joe) =[tex](\frac{1}{2} )[/tex]
[tex]\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})[/tex]
Now, solving for the value of K , we get:
[tex](\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0[/tex]
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.
