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Difficulty: MediumCalculating Distance

A freight train departs from a central hub to deliver materials across two different transit zones. In the primary zone, the train maintains a constant speed of 60 mph60\text{ mph} for 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes}. Upon entering the secondary zone, it reduces its speed to 40 mph40\text{ mph} for the remaining 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes} of the route. What is the total distance traveled by the freight train?

  1. 215 miles215\text{ miles}Answer
  2. B
    200 miles200\text{ miles}
  3. C
    193 miles193\text{ miles}
  4. D
    165 miles165\text{ miles}

Answer

The freight train traveled a total distance of 215 miles215\text{ miles}.
To find the total distance, each segment must be calculated separately using the formula Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}. For the primary zone, 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes} is 2.75 hours2.75\text{ hours}. Multiplying 60 mph60\text{ mph} by 2.75 hours2.75\text{ hours} yields 165 miles165\text{ miles}. For the secondary zone, 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes} is 1.25 hours1.25\text{ hours}. Multiplying 40 mph40\text{ mph} by 1.25 hours1.25\text{ hours} yields 50 miles50\text{ miles}. The total distance is the sum of these two segments: 165+50=215 miles165 + 50 = 215\text{ miles}.

Step-by-Step Solution

1
Convert the travel time for the primary zone into hours.
2 hours and 45 minutes=2+4560=2.75 hours2\text{ hours and } 45\text{ minutes} = 2 + \frac{45}{60} = 2.75\text{ hours}.
Speed is given in miles per hour (mph), so time must be in hours to calculate distance.
2
Calculate the distance traveled in the primary zone.
Distance=Speed×Time=60 mph×2.75 hours=165 miles\text{Distance} = \text{Speed} \times \text{Time} = 60\text{ mph} \times 2.75\text{ hours} = 165\text{ miles}.
Applying the standard distance formula for the first segment.
3
Convert the travel time for the secondary zone into hours.
1 hour and 15 minutes=1+1560=1.25 hours1\text{ hour and } 15\text{ minutes} = 1 + \frac{15}{60} = 1.25\text{ hours}.
Time must be consistently in hours to match the speed unit.
4
Calculate the distance traveled in the secondary zone.
Distance=40 mph×1.25 hours=50 miles\text{Distance} = 40\text{ mph} \times 1.25\text{ hours} = 50\text{ miles}.
Applying the distance formula for the second segment.
5
Add the distances of both zones to find the total distance.
165 miles+50 miles=215 miles165\text{ miles} + 50\text{ miles} = 215\text{ miles}.
The total distance is the sum of all individual legs of the journey.

Key Concept

Calculating distance across multiple segments requires converting time into consistent units (hours) before applying the distance formula (d=rtd = rt) to each segment and summing the results.
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Topics

Calculating Distance

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