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Question

Difficulty: Very hardCalculating Distance

An armored convoy travels from Camp Alpha to Camp Bravo. For the first segment of the trip, the convoy travels at an average speed of 45 mph for 1 hour and 20 minutes. They then stop for a 45-minute rest. After the rest, the convoy resumes travel at an average speed of 30 mph for 2 hours and 15 minutes to reach Camp Bravo. Upon arrival, the convoy immediately takes a different, more direct route back to Camp Alpha. The return route is 20% shorter than the total distance they traveled to reach Camp Bravo. What is the total distance the convoy traveled during the entire round trip?

  1. A
    127.5 miles
  2. B
    153.0 miles
  3. C
    213.3 miles
  4. 229.5 milesAnswer

Answer

229.5 miles
The correct answer accurately synthesizes multiple principles: converting mixed time units into exact hourly fractions, calculating distance for separate legs using D=RTD = RT, applying a percent reduction to find a new distance, and summing all legs to find the aggregate total distance of a round trip.

Step-by-Step Solution

1
Calculate the distance covered during the first travel segment.
6060 miles
Convert 1 hour 20 minutes into hours: 1+2060=1+13=431 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3} hours. Multiply by speed: 45×43=6045 \times \frac{4}{3} = 60 miles.
2
Calculate the distance covered during the second travel segment.
67.567.5 miles
Convert 2 hours 15 minutes into hours: 2+1560=2+14=2.252 + \frac{15}{60} = 2 + \frac{1}{4} = 2.25 hours. Multiply by speed: 30×2.25=67.530 \times 2.25 = 67.5 miles. (The 45-minute rest adds 0 distance).
3
Find the total outbound distance to Camp Bravo.
127.5127.5 miles
Add the distances from the first and second segments: 60+67.5=127.560 + 67.5 = 127.5 miles.
4
Calculate the distance of the return route.
102102 miles
The return route is 20% shorter than the outbound trip. This means it is 100%−20%=80%100\% - 20\% = 80\% of the outbound distance. Multiply: 127.5×0.8=102127.5 \times 0.8 = 102 miles.
5
Calculate the total distance traveled for the entire round trip.
229.5229.5 miles
Add the total outbound distance and the return distance: 127.5+102=229.5127.5 + 102 = 229.5 miles.

Key Concept

Calculating total distance across multiple legs with varying speeds, mixed time units, and percent reductions.
Estimated Time:3m 0s
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Topics

Calculating Distance

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