Question

Karen can wax her SUV in 5 hr. Clarann can wax the same SUV In 8 hr. If they work together, how long will it take them to wax the SUV? Write your answer as a fraction or mixed number, if necessary.

Answer 1

To find how long it will take Karen and Clarann to wax the SUV together, we can find their rates of work and combine them.

1. **Calculate rate for Karen**:
- Karen can wax the SUV in 5 hours, so her rate is:
\[
\text{Rate of Karen} = \frac{1 \text{ SUV}}{5 \text{ hours}} = \frac{1}{5} \text{ SUVs per hour}
\]

2. **Calculate rate for Clarann**:
- Clarann can wax the SUV in 8 hours, so her rate is:
\[
\text{Rate of Clarann} = \frac{1 \text{ SUV}}{8 \text{ hours}} = \frac{1}{8} \text{ SUVs per hour}
\]

3. **Combine their rates**:
- Their combined rate when working together is:
\[
\text{Combined Rate} = \frac{1}{5} + \frac{1}{8}
\]

To add these fractions, we need a common denominator. The least common multiple of 5 and 8 is 40.

Convert each rate:
\[
\frac{1}{5} = \frac{8}{40}
\]
\[
\frac{1}{8} = \frac{5}{40}
\]

Now, we can add the fractions:
\[
\text{Combined Rate} = \frac{8}{40} + \frac{5}{40} = \frac{13}{40} \text{ SUVs per hour}
\]

4. **Find the time to wax one SUV**:
To find the time it takes to wax one SUV together, we take the reciprocal of their combined rate:
\[
\text{Time} = \frac{1 \text{ SUV}}{\frac{13}{40} \text{ SUVs per hour}} = \frac{40}{13} \text{ hours}
\]

5. **Convert to a mixed number**:
Dividing 40 by 13 gives us:
\[
40 \div 13 = 3 \quad \text{with a remainder of } 1
\]
So:
\[
\frac{40}{13} = 3 \frac{1}{13}
\]

Thus, the time it will take Karen and Clarann to wax the SUV together is:
\[
\boxed{\frac{40}{13}} \text{ hours} \text{ or } 3 \frac{1}{13} \text{ hours}
\]