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Difficulty: MediumAverage Speed

A military supply convoy is tasked with delivering equipment to an outpost 210210 miles away. The convoy commander is ordered to maintain an overall average speed of 3535 miles per hour for the entire journey. If the convoy completes the first 9090 miles in 22 hours, what average speed, in miles per hour, must they maintain for the remainder of the trip to exactly meet their overall time target?

Answer: 30 mph

Answer

The convoy must maintain a speed of 30 mph for the remainder of the trip.
The overall target requires the 210210-mile trip to be completed in 66 hours (210÷35210 \div 35). Because the first 9090 miles took 22 hours, there are 120120 miles left to travel and 44 hours remaining to do so. Therefore, the required speed is 120120 miles ÷\div 44 hours = 3030 mph.

Step-by-Step Solution

1
Calculate the total allowable time for the convoy's trip.
Total time = 210÷35=6210 \div 35 = 6 hours.
Overall average speed is the total distance divided by total time. Knowing the total distance and target average speed allows us to find the total time allowed.
2
Calculate the remaining distance for the second part of the trip.
Remaining distance = 210−90=120210 - 90 = 120 miles.
We need to find out how much further the convoy has to travel.
3
Calculate the remaining time available to complete the journey.
Remaining time = 6−2=46 - 2 = 4 hours.
Subtracting the time already spent from the total time gives the time left to cover the remaining distance.
4
Calculate the required average speed for the final leg.
Required speed = 120÷4=30120 \div 4 = 30 mph.
Average speed for any leg is the distance of that leg divided by the time spent on that leg.

Key Concept

Average speed is calculated by dividing the total distance by the total time, and the properties of individual legs (distance and time) sum to the total distance and total time.
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