Question

On average, William takes 2 less hours to assemble a computer than Douglas. If working together William and Douglas can assemble 25 computers in a combined 60 hours, how long does it take Douglas to assemble a computer? Do not include the units in your answer

Answer 1

6 hours

Explanation:

From this we can build the following equation:

60x+60x−2=25

Multiply each side of the equation by the least common denominator x(x−2).

60(x−2)+60x60x−120+60x00=25x(x−2)=25x2−50x=25x2−170x+120=5x2−34x+24

The resulting quadratic can be solved by factoring.

00=5x2−34x+24=(5x−4)(x−6)

Based on this equation, x=45 or x=6. The solution x=45 is extraneous, so x=6. Thus, it takes Douglas x=6 hours to assemble a computer.

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Answer 2

Let x = hours taken by William to assemble a computer.
Let y = hours taken by Douglas to assemble a computer

Because William takes 2 hours less than Douglas to assemble a computer, therefore
x = y - 2

When working together, they assemble 25 computers in 60 hours. Therefore
(x + y hours/computer)*(25 computers) = (60 hours)
25(x + y) = 60
x + y = 2.4

Because x = y - 2, obtain
y - 2 + y = 2.4
2y = 4.4
y = 2.2
x = y - 2 = 2.2 - 2 = 0.2

William takes 0.2 hours (12 minutes) to assemble a computer.
Douglas takes 2.2 hours (or 2 hours, 12 minutes) to assemble a computer.

Answer: 2.2