Question

Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone.


What is the value of r, the part of the lawn that Jing could complete in 1 hour?

0.075
0.125
0.375
0.625

Answer 1

To find the value of \( r \), which represents the fraction of the lawn Jing can complete in one hour, we can start by determining the work rates of Melissa and Jing separately.

1. **Melissa's Work Rate**:
Since Melissa can mow the lawn alone in 8 hours, her work rate is:
\[
\text{Rate of Melissa} = \frac{1 \text{ lawn}}{8 \text{ hours}} = \frac{1}{8} \text{ lawns per hour}
\]

2. **Combined Work Rate of Melissa and Jing**:
Together, Melissa and Jing can mow the lawn in 5 hours, so their combined work rate is:
\[
\text{Combined Rate} = \frac{1 \text{ lawn}}{5 \text{ hours}} = \frac{1}{5} \text{ lawns per hour}
\]

3. **Jing's Work Rate**:
Let \( r \) be the rate at which Jing can mow the lawn alone (in lawns per hour). The equation for their combined work rate can be set up as follows:
\[
\text{Rate of Melissa} + \text{Rate of Jing} = \text{Combined Rate}
\]
Substituting the known values:
\[
\frac{1}{8} + r = \frac{1}{5}
\]

4. **Solve for \( r \)**:
To solve for \( r \), first subtract \(\frac{1}{8}\) from both sides:
\[
r = \frac{1}{5} - \frac{1}{8}
\]

To perform this subtraction, we need a common denominator, which is 40:
\[
\frac{1}{5} = \frac{8}{40}, \quad \frac{1}{8} = \frac{5}{40}
\]
So:
\[
r = \frac{8}{40} - \frac{5}{40} = \frac{3}{40}
\]

5. **Calculate \( r \)**:
Now we calculate the decimal equivalent of \( r \):
\[
r = \frac{3}{40} = 0.075
\]

Thus, the value of \( r \), the part of the lawn that Jing could complete in 1 hour, is \( 0.075 \).

The answer is:
\[
\boxed{0.075}
\]