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Difficulty: MediumAverage Speed

An armored cavalry troop conducts a training movement. They travel 4545 miles over rough terrain at a speed of 1515 miles per hour. After a 9090-minute halt for vehicle maintenance, they proceed 7575 miles along a highway at 5050 miles per hour. What is their overall average speed, in miles per hour, for the entire operation?

Answer: 20 mph

Answer

The overall average speed is 2020 miles per hour.
The correct answer is 2020 because average speed is the ratio of total distance to total time. The total distance is 120120 miles (45+7545 + 75). The total time includes the travel times (33 hours and 1.51.5 hours) plus the maintenance halt (1.51.5 hours), which equals 66 hours. Dividing 120120 miles by 66 hours gives an overall average speed of 2020 miles per hour.

Step-by-Step Solution

1
Calculate the time taken for the first travel segment.
4515=3\frac{45}{15} = 3 hours
Time is required to determine the total elapsed time of the operation.
2
Convert the maintenance halt time from minutes to hours.
9090 minutes =1.5= 1.5 hours
All time units must be consistent (hours) before they can be added together.
3
Calculate the time taken for the second travel segment.
7550=1.5\frac{75}{50} = 1.5 hours
This gives the travel time for the final leg of the route.
4
Calculate the total distance traveled.
45+75=12045 + 75 = 120 miles
Total distance is the numerator in the average speed formula.
5
Calculate the total elapsed time for the entire operation.
3+1.5+1.5=63 + 1.5 + 1.5 = 6 hours
Total time is the denominator in the average speed formula, and it must include the maintenance halt.
6
Calculate the overall average speed.
1206=20\frac{120}{6} = 20 miles per hour
Average speed is defined as the total distance divided by the total time.

Key Concept

Average speed is calculated by dividing the total distance traveled by the total time elapsed, including any rest stops or delays.
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