A high-speed passenger train is scheduled to travel a 300-mile route between two cities wi… — Armed Services Vocational Aptitude Battery (ASVAB)

A high-speed passenger train is scheduled to travel a $300$ -mile route between two cities with an overall average speed of $60$ miles per hour. During the first leg of the trip, the train travels $150$ miles at an average speed of $50$ miles per hour. At what average speed must the train travel for the remaining $150$ miles to meet its scheduled overall average speed?

75 mphCevap
B
70 mph
C
100 mph
D
30 mph

Cevap

The train must travel at 75 mph for the remaining distance.

To solve for the required speed, you must work with time. The entire 300-mile trip at an average of 60 mph allows a total of 5 hours (

300 \div 60 = 5

). The first 150 miles at 50 mph consumed 3 hours (

150 \div 50 = 3

). This leaves exactly 2 hours to cover the remaining 150 miles. Dividing the remaining distance by the remaining time (

150 \div 2

) gives the necessary speed of 75 mph.

Adım Adım Çözüm

Calculate the total time allowed for the entire trip.

300 \text{ miles} \div 60 \text{ mph} = 5 \text{ hours}

Average speed is defined as total distance divided by total time. We need the total time limit to figure out how much time is left.

Calculate the time spent on the first leg of the trip.

150 \text{ miles} \div 50 \text{ mph} = 3 \text{ hours}

Using the distance and speed given for the first segment, we determine how much of our total time budget has been used.

Determine the time remaining for the second leg.

5 \text{ hours} - 3 \text{ hours} = 2 \text{ hours}

Subtracting the time already used from the total allowed time gives the time remaining to complete the journey.

Calculate the required average speed for the remaining distance.

150 \text{ miles} \div 2 \text{ hours} = 75 \text{ mph}

Speed is distance divided by time. Applying this to the remaining segment gives the required speed.

Anahtar Kavram

To find an unknown speed in a multi-segment trip, you must base calculations on Total Distance and Total Time, rather than averaging the individual speeds.

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