A high-speed passenger train travels between two major cities. It covers the first segment… — Armed Services Vocational Aptitude Battery (ASVAB)

A high-speed passenger train travels between two major cities. It covers the first segment of the journey at an average speed of $120\text{ mph}$ for $1\text{ hour and } 45\text{ minutes}$ . Due to track maintenance, it reduces its speed to $40\text{ mph}$ for $36\text{ minutes}$ . After clearing the maintenance zone, it accelerates and travels at $150\text{ mph}$ for $48\text{ minutes}$ to reach its final destination. What is the total distance of the trip?

354 milesCevap
B
260.4 miles
C
325.5 miles
D
330 miles

Cevap

354 miles

The total distance is found by calculating the distance of each leg separately and adding them together. First, convert all minute values into hours by dividing by 60 (

1\text{ hr } 45\text{ min} = 1.75\text{ hr}

;

36\text{ min} = 0.6\text{ hr}

;

48\text{ min} = 0.8\text{ hr}

). Then, multiply each time by its corresponding speed to find the distances:

120 \times 1.75 = 210\text{ miles}

;

40 \times 0.6 = 24\text{ miles}

; and

150 \times 0.8 = 120\text{ miles}

. Adding these together gives

210 + 24 + 120 = 354\text{ miles}

Adım Adım Çözüm

Convert the travel time for the first segment into hours.

45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}

. Total time

= 1.75\text{ hours}

Speed is given in miles per hour (mph), so time must be in hours to calculate distance correctly.

Calculate the distance covered in the first segment.

Distance

= 120\text{ mph} \times 1.75\text{ hours} = 210\text{ miles}

Applying the formula Distance = Rate × Time for the first leg of the journey.

Convert the time and calculate the distance for the second (maintenance) segment.

Time

= \frac{36}{60}\text{ hours} = 0.6\text{ hours}

. Distance

= 40\text{ mph} \times 0.6\text{ hours} = 24\text{ miles}

The second segment has a different speed and time that must be evaluated independently.

Convert the time and calculate the distance for the final segment.

Time

= \frac{48}{60}\text{ hours} = 0.8\text{ hours}

. Distance

= 150\text{ mph} \times 0.8\text{ hours} = 120\text{ miles}

The final segment has its own rate and duration to calculate.

Sum the distances of all segments to find the total distance.

210 + 24 + 120 = 354\text{ miles}

The total distance of a multi-leg journey is the sum of the distances of the individual legs.

Anahtar Kavram

Calculating distance using mixed time units across multiple journey segments

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