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Difficulty: MediumCalculating Rate and Time

A riverine patrol boat is tasked with delivering supplies to a forward operating base. The boat needs to cover a distance of 3.53.5 miles upstream. If it maintains a constant speed over ground of 1414 miles per hour and departs at 09450945 hours, at what time will the boat arrive at its destination?

  1. A
    12151215 hours
  2. 10001000 hoursAnswer
  3. C
    13451345 hours
  4. D
    10101010 hours

Answer

The boat will arrive at 10001000 hours.
To find the arrival time, first calculate the travel time. Using the formula Time = Distance / Rate, the time is 3.5/14=0.253.5 / 14 = 0.25 hours. Next, convert 0.250.25 hours to minutes by multiplying by 6060, which equals 1515 minutes. Finally, add the 1515 minutes of travel time to the departure time of 09450945 hours. Adding 1515 minutes to 09450945 brings the clock time exactly to 10001000 hours.

Step-by-Step Solution

1
Calculate the travel time in hours by dividing the distance by the rate.
t=3.5 miles14 mph=0.25 hourst = \frac{3.5 \text{ miles}}{14 \text{ mph}} = 0.25 \text{ hours}
The formula for time is Time = Distance / Rate.
2
Convert the calculated time from hours to minutes.
0.25 hours×60 minutes/hour=15 minutes0.25 \text{ hours} \times 60 \text{ minutes/hour} = 15 \text{ minutes}
Clock time additions are easier and more accurate when working with minutes rather than fractional hours.
3
Add the travel time in minutes to the departure time to find the arrival time.
0945 hours+15 minutes=1000 hours0945 \text{ hours} + 15 \text{ minutes} = 1000 \text{ hours}
The arrival time is the departure time plus the elapsed travel time. Adding 15 minutes to 45 minutes completes the 60-minute hour, rolling the time over to 1000.

Key Concept

Calculating elapsed time using the distance formula (t=d/rt = d/r) and converting fractional hours to minutes to determine clock arrival time.
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Topics

Calculating Rate and Time

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