An armored reconnaissance vehicle is conducting a route clearance mission. It travels at a… — Armed Services Vocational Aptitude Battery (ASVAB)

An armored reconnaissance vehicle is conducting a route clearance mission. It travels at a steady speed of $32\text{ miles per hour}$ for $45\text{ minutes}$ . Then, due to rough terrain, its speed drops to $16\text{ miles per hour}$ for the next $1\text{ hour}$ and $15\text{ minutes}$ . What is the total distance the vehicle traveled, in miles?

Cevap: 44 / 44 miles / 44 mi / forty-four / 44.0

Cevap

44 miles

To find the total distance traveled, we evaluate each leg of the trip using the formula Distance = Rate × Time. The first leg is driven at 32 mph for 45 minutes (which is 0.75 hours). Distance = 32 × 0.75 = 24 miles. The second leg is driven at 16 mph for 1 hour and 15 minutes (which is 1.25 hours). Distance = 16 × 1.25 = 20 miles. The total distance is the sum of these two segments: 24 + 20 = 44 miles.

Adım Adım Çözüm

Convert the travel time of the first leg from minutes to hours.

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

The speed is given in miles per hour, so the time must be in hours to calculate the distance properly.

Calculate the distance covered during the first leg.

32\text{ mph} \times 0.75\text{ hours} = 24\text{ miles}

Using the formula Distance = Rate × Time.

Convert the travel time of the second leg to hours.

1\text{ hour}

and

15\text{ minutes} = 1 + \frac{15}{60}\text{ hours} = 1.25\text{ hours}

Time must be consistently in hours to match the rate of 16 mph.

Calculate the distance covered during the second leg.

16\text{ mph} \times 1.25\text{ hours} = 20\text{ miles}

Using the formula Distance = Rate × Time.

Add the distances of both legs to find the total distance.

24\text{ miles} + 20\text{ miles} = 44\text{ miles}

The total distance is the sum of the individual segments.

Anahtar Kavram

Calculating distance across multiple journey segments requiring time unit conversions.

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