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Zorluk: OrtaCalculating Distance

A disaster relief team is transporting supplies to a stricken area. They first drive their trucks on a paved highway at a constant speed of 52 miles per hour52\text{ miles per hour} for 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes}. They then transition to rough off-road terrain, where they travel at a steady speed of 18 miles per hour18\text{ miles per hour} for 40 minutes40\text{ minutes} to reach their final destination. What is the total distance traveled by the team?

  1. A
    65 miles65\text{ miles}
  2. B
    67 miles67\text{ miles}
  3. 77 miles77\text{ miles}Cevap
  4. D
    4,620 miles4,620\text{ miles}

Cevap

The correct total distance is 77 miles77\text{ miles}.
The total distance is the sum of the distances from both legs of the trip. The first leg is 1 hour and 15 minutes (1.25 hours) at 52 mph, which equals 65 miles. The second leg is 40 minutes (2/3 of an hour) at 18 mph, which equals 12 miles. Adding these gives a total of 77 miles.

Adım Adım Çözüm

1
Convert the travel time for the first leg into hours.
1 hour and 15 minutes=11560 hours=1.25 hours1\text{ hour and } 15\text{ minutes} = 1\frac{15}{60}\text{ hours} = 1.25\text{ hours}.
Speed is given in miles per hour, so time must be converted into hours to correctly calculate the distance.
2
Calculate the distance traveled during the first leg.
52 mph×1.25 hours=65 miles52\text{ mph} \times 1.25\text{ hours} = 65\text{ miles}.
Distance equals rate multiplied by time (D=R×TD = R \times T).
3
Convert the travel time for the second leg into hours.
40 minutes=4060 hours=23 hours40\text{ minutes} = \frac{40}{60}\text{ hours} = \frac{2}{3}\text{ hours}.
Consistent units are required for the second leg's calculation.
4
Calculate the distance traveled during the second leg.
18 mph×23 hours=12 miles18\text{ mph} \times \frac{2}{3}\text{ hours} = 12\text{ miles}.
Using the D=R×TD = R \times T formula for the off-road section.
5
Add the distances of both legs to find the total distance.
65 miles+12 miles=77 miles65\text{ miles} + 12\text{ miles} = 77\text{ miles}.
The question asks for the total combined distance traveled by the team to reach their destination.

Anahtar Kavram

Calculating total distance for multi-leg journeys by applying the D=R×TD = R \times T formula with necessary time unit conversions.
Tahmini Süre:1m 30s
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Calculating Distance

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