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unknown9263
07.03.2020 •
Mathematics
Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How long would it take each of them to do the job alone?
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Ответ:
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 =![(\frac{1}{K})](/tpl/images/0537/5589/8f449.png)
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 =![(\frac{1}{K-3})](/tpl/images/0537/5589/3573f.png)
Now, when both of them wok together, it takes them 2 hours.
So, the per hour rate of BOTH of them =![(\frac{1}{2})](/tpl/images/0537/5589/b827e.png)
⇒ Per hour rate of ( Dwight + Joe) =![(\frac{1}{2} )](/tpl/images/0537/5589/82f9c.png)
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.
Ответ:
ContentBot2
Step-by-step explanation: