Question

Wilma can mow the lawn in 4 hours. If Kyle helps her with another mower, the lawn can be mowed in 3 hours. How many hours would it take Kyle if he worked alone?

Answer 1

12 hours

Explanation:

Let w = Wilma alone

Let k = Kyle alone

Let t = Working together

Given the following data;

Time it took Wilma = 4 hours

Time it took them together = 3 hours

Time it took Kyle = x

To find the time it will take Kyle, we would use this arithmetical expression;

`\frac {1}{w} + \frac {1}{k} = \frac {1}{t}`

Substituting into the equation, we have;

`\frac {1}{4} + \frac {1}{x} = \frac {1}{3}`

Lowest common denominator (LCD) = 12x

Multiplying all through by "12x" we have;

`12x * \frac {1}{4} + 12x * \frac {1}{x} = 12x * \frac {1}{3}`

Simplifying the equation, we have;

`3x + 12 = 4x`

Rearranging the equation, we have;

`4x - 3x = 12`

x = 12 hours.

Therefore, it would take Kyle 12 hours to mow if he worked alone.