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Difficulty: Very hardCalculating Distance

A logistics convoy leaves a supply depot and travels at a steady speed of 40 miles per hour for 2 hours and 15 minutes. After a 45-minute halt to refuel, the convoy resumes its route at a speed that is 20% faster than its initial speed. It travels at this new speed for 1 hour and 40 minutes until reaching the forward operating base. What is the total distance traveled by the convoy, in miles?

Answer: 170 / 170 miles / 170 mi

Answer

170
The correct answer is found by breaking the journey into two separate legs of movement, converting all times to hours, calculating the distance for each leg independently using their respective speeds, and summing the results.

Step-by-Step Solution

1
Calculate the time traveled during the first leg in hours.
2 hours and 15 minutes is equivalent to 2.25 hours.
Since the speed is given in miles per hour, time must be expressed in hours.
2
Calculate the distance covered during the first leg.
40 mph × 2.25 hours = 90 miles.
Using the distance formula d=r×td = r \times t.
3
Determine the speed of the convoy for the second leg.
40 mph + (0.20 × 40 mph) = 40 + 8 = 48 mph.
The problem states the convoy travels 20% faster after the halt.
4
Calculate the time traveled during the second leg in hours.
1 hour and 40 minutes is equivalent to 140601 \frac{40}{60} hours, which simplifies to 53\frac{5}{3} hours.
Converting mixed time units to a single fraction of hours is necessary for accurate calculation.
5
Calculate the distance covered during the second leg.
48 mph × 53\frac{5}{3} hours = 80 miles.
Using the distance formula d=r×td = r \times t.
6
Calculate the total distance traveled.
90 miles + 80 miles = 170 miles.
The total distance is the sum of the distances from the two active travel legs. The 45-minute halt added 0 miles.

Key Concept

Calculating distance across multiple legs with varying speeds and mixed time units.
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Topics

Calculating Distance

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