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Difficulty: Very hardCalculating Rate and Time

A military convoy must complete a 180-mile route to a forward operating base in exactly 4 hours. The convoy travels at an average speed of 50 mph for 90 minutes, then halts for a 60-minute security checkpoint. What average speed, in mph, must the convoy maintain for the remainder of the journey to arrive exactly on time?

  1. A
    42
  2. B
    45
  3. C
    54
  4. 70Answer

Answer

70
The convoy has already traveled 75 miles in 1.5 hours, and stopped for 1.0 hour. This means 2.5 hours have elapsed in total, leaving 1.5 hours to travel the remaining 105 miles. Dividing 105 miles by 1.5 hours results in a required speed of 70 mph.

Step-by-Step Solution

1
Convert the travel and checkpoint times from minutes to hours.
90 minutes = 1.5 hours; 60 minutes = 1.0 hour.
Speed is given in miles per hour (mph), so time must be uniformly expressed in hours.
2
Calculate the distance covered during the first leg of the journey.
50 mph × 1.5 hours = 75 miles.
This establishes how much of the 180-mile route has already been completed before the stop.
3
Determine the remaining distance to the base.
180 miles - 75 miles = 105 miles.
This is the distance that must be covered in the final driving leg.
4
Calculate the time remaining to complete the route.
4 hours - (1.5 hours + 1.0 hour) = 4 - 2.5 = 1.5 hours.
The convoy must arrive exactly 4 hours after initial departure, accounting for both active driving and stopped time.
5
Calculate the required average speed for the final leg.
105 miles ÷ 1.5 hours = 70 mph.
Rate equals distance divided by time.

Key Concept

Calculating Rate and Time
Estimated Time:2m 30s
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Topics

Calculating Rate and Time

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