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Question

Difficulty: MediumRound Trips

A delivery truck travels from a warehouse to a distribution center at an average speed of 4040 mph and returns along the same route at an average speed of 6060 mph. If the entire round trip takes 55 hours, what is the total round-trip distance traveled by the truck?

  1. A
    120120 miles
  2. 240240 milesAnswer
  3. C
    250250 miles
  4. D
    500500 miles

Answer

The correct total round-trip distance is 240240 miles.
The total time is the sum of the time for each leg. Letting dd be the one-way distance, the equation is d40+d60=5\frac{d}{40} + \frac{d}{60} = 5. Solving this gives a one-way distance of d=120d = 120 miles. Since the question asks for the total round-trip distance, this must be doubled to get 240240 miles.

Step-by-Step Solution

1
Set up an equation for the total time of the trip.
Let dd be the one-way distance. Time is equal to Distance divided by Speed. Therefore, the total time equation is d40+d60=5\frac{d}{40} + \frac{d}{60} = 5.
The total round-trip time is the sum of the time spent on the outbound leg and the return leg.
2
Find a common denominator to add the fractions.
The least common multiple of 4040 and 6060 is 120120. Convert the fractions: 3d120+2d120=5\frac{3d}{120} + \frac{2d}{120} = 5.
Fractions must have a common denominator before they can be algebraically combined.
3
Combine the fractions and solve for the one-way distance dd.
5d120=5\frac{5d}{120} = 5, which simplifies to d24=5\frac{d}{24} = 5. Multiplying both sides by 2424 yields d=120d = 120 miles.
This isolates the variable dd to determine the distance of a single leg of the journey.
4
Calculate the total round-trip distance.
Total distance = 2d=2×120=2402d = 2 \times 120 = 240 miles.
The question specifically asks for the total round-trip distance, which is twice the one-way distance.

Key Concept

To find distances in round trips with different speeds, set up an equation using the relationship Time = Distance / Speed for each leg, taking care to answer the specific question asked (one-way vs. total distance).
Estimated Time:1m 30s
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Topics

Round Trips

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