Question

Working together, two people can cut a large lawn in 2 hrs. One person can do the job alone in 3 hr less time than the other. How long would it take the faster person to do

the job? (Let x represent the time of the faster person.)
Faster worker
Slower worker
Rate
Time working
together
2
2
Fractional part
of the job done
The faster person would do the job alone in hours.
(Round to the nearest tenth as needed.)

Answer 1

By setting up an equation with the combined work rates of the faster and slower workers, we can solve for the time it takes for the faster worker to complete the job alone, which is 3 hours.

Step-by-step explanation:

To find how long it would take the faster person to do the job alone, we use the information that together they can complete the job in 2 hours and that one person can do it in 3 hours less time than the other. Let x represent the number of hours the faster worker can complete the job alone. The slower worker then takes x + 3 hours to complete the job alone.

The work rates of the faster and slower workers are 1/x and 1/(x + 3) respectively (since work rate is inversely proportional to time). Working together, their combined work rate is 1/2 since they complete the job in 2 hours.

The equation representing their combined work rates when working together is:

1/x + 1/(x + 3) = 1/2

To solve for x, first find a common denominator, which is 2x(x + 3), and then combine like terms:

• 2(x + 3) + 2x = x(x + 3)
• 2x + 6 + 2x = x^2 + 3x
• 4x + 6 = x^2 + 3x
• x^2 - x - 6 = 0

Factoring the quadratic equation gives us:

• (x - 3)(x + 2) = 0

Since time cannot be negative, the suitable solution for x is 3 hours.

The faster person would take 3 hours to do the job alone.