Question

Difficulty: MediumCalculating Rate and Time

A logistics battalion is coordinating different transport missions. Match each vehicle's specific mission profile with its correct calculated travel time, average speed, or arrival time.

  • A supply truck travels a distance of 9090 miles at a constant speed of 4040 mph.Total travel time of 22 hours and 1515 minutes
  • A patrol boat covers a distance of 135135 miles in exactly 4.54.5 hours.Average speed of 3030 mph
  • An armored transport departs at 0800 hours and travels 165165 miles at an average speed of 5555 mph.Arrival time of 1100 hours
  • A medical evacuation helicopter flies a distance of 7575 miles in exactly 3030 minutes.Average speed of 150150 mph

Answer

The logistics mission profiles match successfully by applying the distance formula and executing necessary time conversions (e.g., 2.252.25 hours is 22 hours and 1515 minutes, and 3030 minutes is 0.50.5 hours).
Each match strictly follows the distance formula d=r×td = r \times t, correctly manipulating the variables and converting fractional hours to minutes or minutes to hours where required.

Step-by-Step Solution

1
Calculate the travel time for the supply truck.
Total travel time of 22 hours and 1515 minutes
Applying t=d÷rt = d \div r (90÷40=2.2590 \div 40 = 2.25 hours) and converting the decimal remainder to minutes (0.25×60=150.25 \times 60 = 15).
2
Calculate the average speed of the patrol boat.
Average speed of 3030 mph
Applying r=d÷tr = d \div t (135÷4.5=30135 \div 4.5 = 30).
3
Calculate the arrival time of the armored transport.
Arrival time of 1100 hours
Applying t=d÷rt = d \div r (165÷55=3165 \div 55 = 3 hours), then adding 33 hours to 0800 hours.
4
Calculate the average speed of the medevac helicopter.
Average speed of 150150 mph
Converting 3030 minutes to 0.50.5 hours, then applying r=d÷tr = d \div t (75÷0.5=15075 \div 0.5 = 150).

Key Concept

Applying the fundamental distance relationship (d=r×td = r \times t) to calculate unknown rates and times, while managing unit conversions and clock mathematics.
Estimated Time:2m 0s
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