A home coming device left its home to deliver a message. On takeoff, the device encountered a tailwind of 9 mph and made the delivery in 15 minutes. The return trip into the win took 30 minutes. How fast the device fly in still air?

Question

Mathematics

Amira Meadows

8 May, 21:32

A home coming device left its home to deliver a message. On takeoff, the device encountered a tailwind of 9 mph and made the delivery in 15 minutes. The return trip into the win took 30 minutes. How fast the device fly in still air?

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Answers (1)

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Evony · Answer 1

Answer: the device flies at 27 mph in still air

Step-by-step explanation:

Let x represent the speed of the home coming device in still air.

On takeoff, the device encountered a tailwind of 9 mph and made the delivery in 15 minutes (15/60 = 0.25 hours). It is assumed that it travelled in the direction of the wind. This mean that the total speed would be

(x + 9) mph

Distance travelled = speed * time

Therefore, distance covered during delivery would be

0.25 (x + 9)

The return trip into the wind took 30 minutes (30/60 = 0.5 hours). This means that it travelled against the wind direction. The total speed would be (x - 9) mph.

Distance travelled on returning would be

0.5 (x - 9)

Since the distance travelled is the same, then

0.25 (x + 9) = 0.5 (x - 9)

0.25x + 2.25 = 0.5x - 4.5

0.5x - 0.25x = 2.25 + 4.5

0.25x = 6.75

x = 6.75/0.25

x = 27 mph