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Zorluk: ZorCalculating Rate and Time

A supply train needs to deliver equipment to a base that is 110 miles away. For the first 1 hour and 20 minutes, the train travels at a steady rate of 30 mph. Due to track repairs, the train must travel at exactly 20 mph for the remainder of the trip. What is the total travel time from the start of the journey until the train arrives at the base?

  1. A
    4 hours and 24 minutes
  2. B
    3 hours and 30 minutes
  3. C
    4 hours and 54 minutes
  4. 4 hours and 50 minutesCevap

Cevap

The total travel time is 4 hours and 50 minutes.
The correct answer is found by first determining that the train travels 40 miles during its initial 1 hour and 20 minutes (30 mph×113 hours30 \text{ mph} \times 1 \frac{1}{3} \text{ hours}). With 70 miles remaining from the 110-mile total (110−40110 - 40), traveling at 20 mph takes exactly 3.5 hours, or 3 hours and 30 minutes. Adding the duration of both legs (1 hour 20 minutes+3 hours 30 minutes1 \text{ hour } 20 \text{ minutes} + 3 \text{ hours } 30 \text{ minutes}) results in a total travel time of 4 hours and 50 minutes.

Adım Adım Çözüm

1
Calculate the distance covered in the first leg of the journey.
The train travels 40 miles in the first leg.
Since 1 hour and 20 minutes is equivalent to 1131 \frac{1}{3} hours (or 43\frac{4}{3} hours), multiplying the rate of 30 mph by this time gives 30×43=4030 \times \frac{4}{3} = 40 miles.
2
Determine the remaining distance to the base.
There are 70 miles remaining.
Subtracting the distance covered from the total distance (110−40=70110 - 40 = 70) gives the remaining travel distance.
3
Calculate the time required for the second leg of the journey.
The second leg takes 3 hours and 30 minutes.
Dividing the remaining distance by the new speed (70÷2070 \div 20) results in 3.5 hours, which equals 3 hours and 30 minutes.
4
Add the time of both legs to find the total travel time.
The total travel time is 4 hours and 50 minutes.
Adding the initial 1 hour and 20 minutes to the second leg's 3 hours and 30 minutes gives 4 hours and 50 minutes.

Anahtar Kavram

Calculating total elapsed time for multi-leg journeys by tracking distance and converting time units properly.
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Konular

Calculating Rate and Time

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