A medical supply drone is programmed to complete a 120-mile delivery route with a required… — Armed Services Vocational Aptitude Battery (ASVAB)

A medical supply drone is programmed to complete a $120$ -mile delivery route with a required overall average speed of $40$ miles per hour. During the first segment, the drone flies $60$ miles at an average speed of $30$ miles per hour. It then lands for a $20$ -minute battery swap. At what average speed must the drone fly for the remainder of the route to achieve its required overall average speed?

A
$50$ mph
B
$60$ mph
$90$ mphCevap
D
$150$ mph

Cevap

The drone must fly at

90

mph for the remainder of the route.

To solve for a missing speed when an overall average is required, you must first find the total time allowed. For a

120

-mile trip at

40

mph, the drone has exactly

3

hours. The first leg took

2

hours (

60

miles

\div

30

mph), and the battery swap took

20

minutes. This leaves only

40

minutes (which is

2/3

of an hour) to travel the remaining

60

miles. Dividing

60

miles by

2/3

hours yields a required speed of

90

mph.

Adım Adım Çözüm

Calculate the total time allowed for the entire trip.

T_{total} = 120 \text{ miles} \div 40 \text{ mph} = 3 \text{ hours}

Overall average speed equals total distance divided by total time.

Calculate the time spent flying the first segment.

T_1 = 60 \text{ miles} \div 30 \text{ mph} = 2 \text{ hours}

Time equals distance divided by speed.

Determine the total time used so far, including the battery swap.

2 \text{ hours} + 20 \text{ minutes} = 2 \text{ hours and } 20 \text{ minutes}

Rest stops and delays must be included in total transit time.

Calculate the remaining time available.

3 \text{ hours} - 2 \text{ hours } 20 \text{ minutes} = 40 \text{ minutes}

Subtract the time already used from the total time allowed.

Convert the remaining time into hours.

40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

Speed is required in miles per hour, so time must be in hours.

Calculate the remaining distance.

120 \text{ miles} - 60 \text{ miles} = 60 \text{ miles}

Subtract the distance already covered from the total distance.

Calculate the required average speed for the final segment.

V_2 = 60 \text{ miles} \div \frac{2}{3} \text{ hours} = 60 \times \frac{3}{2} = 90 \text{ mph}

Speed equals remaining distance divided by remaining time.

Anahtar Kavram

Average speed over a multi-segment journey is defined solely as the total distance divided by the total time. All stops, breaks, and varying speeds must be accounted for by combining their respective times.

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