To solve this problem, we need to determine how frequently Edwin and Hewitt can drop their luggage and record the results together.
-
Determine the individual recording rates:
- Edwin can drop and record once every 4 minutes.
- Hewitt can drop and record once every 5 minutes.
-
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: \[ \text{Combined Rate} = 0.25 + 0.20 = 0.45 \text{ drops per minute} \]
-
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.