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inn [45]
3 years ago
15

Jake can cut and split a cord of 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?
Mathematics
1 answer:
Luba_88 [7]3 years ago
3 0

Answer:

18 hours for Dwight, 9 hours for Jake

Step-by-step explanation:

If J is the time it takes for Jake working alone, and D is the time it takes for Dwight working alone, then:

J = D − 9

Working together, Jake's speed plus Dwight's speed equals 1 cord per 6 hours.

1 / J + 1 / D = 1 / 6

Solve the system of equations by substituting for J:

1 / (D − 9) + 1 / D = 1 / 6

Multiply both sides by D − 9.

1 + (D − 9) / D = (D − 9) / 6

Multiply both sides by D:

D + D − 9 = D (D − 9) / 6

Simplify and solve:

2D − 9 = (D² − 9D) / 6

12D − 54 = D² − 9D

0 = D² − 21D + 54

0 = (D − 3) (D − 18)

D = 3 or 18

Since J = D − 9, D must be greater than 9.  So D = 18 and J = 9.

That means it takes Dwight 18 hours working alone, and it takes Jake 9 hours working alone.

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1st attachment: 

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4 0
3 years ago
Read 2 more answers
You have a large container of mustard oil.You have used 480 quarts of oil. 76% of the oil remains. How many quarts remain?
DiKsa [7]
The best approach to take here is to find out what 1% and 10% are, then multiply them accordingly. 
To find 10%, just divide the amount of quarts by 10.
480/10= 48
Therefore, 10% is 48 quarts.
To find 1%, you then divide the 10% by 10. 
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you then need to find the odd 6%.
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As you're looking for the remainder, you then need to take this away from 480.
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