A commercial cargo drone flies from Base Alpha to Outpost Bravo against a headwind at a co… — GMAT

A commercial cargo drone flies from Base Alpha to Outpost Bravo against a headwind at a constant speed of $30$ miles per hour. On the return flight along the exact same route, traveling with a tailwind, the drone maintains a constant speed of $60$ miles per hour. If the drone spent a total of $3$ hours in flight for the entire round trip, what was its average speed, in miles per hour, for the complete trip?

A
$36$
$40$ Cevap
C
$45$
D
$50$
E
$60$

Cevap

The average speed of the drone for the entire round trip is

40

miles per hour.

The average speed is calculated as total distance divided by total time. Since the one-way distance is

60

miles, the total round-trip distance is

120

miles. Dividing

120

miles by the total time of

3

hours yields

40

miles per hour.

Adım Adım Çözüm

Set up distance and time relationships for each leg of the trip.

Let

d

be the distance in miles between Base Alpha and Outpost Bravo. Time taken for the outbound leg is

t_1 = \frac{d}{30}

hours, and time taken for the return leg is

t_2 = \frac{d}{60}

hours.

Time equals distance divided by rate (

t = \frac{d}{r}

Express total time in terms of

d

and solve for

d

Total time

T = t_1 + t_2 = \frac{d}{30} + \frac{d}{60} = \frac{3d}{60} = \frac{d}{20}

. Given total time is

3

hours,

\frac{d}{20} = 3 \implies d = 60

miles.

Summing the times for both legs equals the total flight time given in the problem.

Calculate the total distance and average speed.

Total distance

= 2d = 2 \times 60 = 120

miles. Average speed

= \frac{\text{Total Distance}}{\text{Total Time}} = \frac{120}{3} = 40

miles per hour.

Average speed for any multi-leg trip is always defined as total distance divided by total time.

Anahtar Kavram

Average Speed for a Round Trip

Tahmini Süre:1m 30s

Soru

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