Question

Edwin and Hewitt are product testers and indestructible luggage incorporated. Edwin can drop a piece of luggage off the top of headquarters and then record the results once every 4 minutes. Hewitt can do the same once every 5 minutes. How many minutes will it take them together to drop their luggage and record the results a (combined) total of 18 times?

Answer 1

To solve this problem, we need to determine how frequently Edwin and Hewitt can drop their luggage and record the results together.

1. **Determine the individual recording rates**:
- Edwin can drop and record once every 4 minutes.
- Hewitt can drop and record once every 5 minutes.

2. **Calculate their combined rate**:
- The rate of Edwin can be expressed as:
\[
\text{Rate of Edwin} = \frac{1 \text{ drop}}{4 \text{ minutes}} = 0.25 \text{ drops per minute}
\]
- The rate of Hewitt can be expressed as:
\[
\text{Rate of Hewitt} = \frac{1 \text{ drop}}{5 \text{ minutes}} = 0.20 \text{ drops per minute}
\]
- Their combined rate of dropping and recording is:
\[
\text{Combined Rate} = 0.25 + 0.20 = 0.45 \text{ drops per minute}
\]

3. **Determine how many minutes it takes to record 18 drops**:
- If they record at a combined rate of 0.45 drops per minute, we can find the time (\(t\)) it takes to record a total of 18 drops using the equation:
\[
t = \frac{\text{Total Drops}}{\text{Combined Rate}} = \frac{18 \text{ drops}}{0.45 \text{ drops per minute}}
\]

- Performing the calculation:
\[
t = \frac{18}{0.45} = 40 \text{ minutes}
\]

Thus, it will take Edwin and Hewitt a total of **40 minutes** to drop their luggage and record the results a combined total of 18 times.