Solve the problem.
-Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 3 hours. How long will it take them to do the job working together?
A) 6 hours
B) $\frac { 1 } { 6 }$ hours
C) $1 \frac { 1 } { 5 }$ hours
D) $\frac { 1 } { 5 }$ hours

Question

Quizplus · Accepted Answer

We can use the formula:
$$\text{time} = \frac{\text{amount of work}}{\text{rate}}$$

Let's assume that the amount of work is 1 (raking all the leaves) and let's find the rates of Martha and her brother:

Martha's rate = amount of work ÷ time = 1 ÷ 2 = 0.5
Brother's rate = amount of work ÷ time = 1 ÷ 3 = 0.333...

Working together, their rate is the sum of their individual rates:
Rate working together = 0.5 + 0.333... = 0.833...

Now we can plug the rate into the formula and solve for time:
$$\text{time} = \frac{\text{amount of work}}{\text{rate}} = \frac{1}{0.833...} \approx 1 \frac{1}{5}$$

Therefore, it will take Martha and her brother $1 \frac { 1 } { 5 }$ hours to rake all the leaves together.

Solve the Problem 16\frac { 1 } { 6 }61​ Hours C)

Solve the Problem $\frac { 1 } { 6 }$ Hours
C)