A flyer on a reconnaissance flight has 4 hours for a round trip. his blade can fly 200 mph in still air. he flies out from his base against a 20 mph wind and immediately returns to his base, flying with the same wind. how many hours did he take for his fight out?

Question

Mathematics

Caitlin Henderson

4 August, 13:54

A flyer on a reconnaissance flight has 4 hours for a round trip. his blade can fly 200 mph in still air. he flies out from his base against a 20 mph wind and immediately returns to his base, flying with the same wind. how many hours did he take for his fight out?

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Answers (1)

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Cale Douglas · Answer 1

When flying with the wind, the effective plane speed is 200 + 20 = 220 mph.

When flying against the wind, the effective plane speed is 200 - 10 = 180 mph.

Let d = the distance (miles) from his base to the destination.

The time (hours) to travel with the wind is

t₁ = d/220

The time (hours) to travel against the wind is

t₂ = d/180

The total time taken is 4 hours, therefore

t₁ + t₂ = 4

d/220 + d/180 = 4

d (1/220 + 1/180) = 4

0.010101d = 4

d = 396 miles

Therefore

t₁ = 396/220 = 1.8 hours = 1 hour, 48 minutes (floght in)

t₂ = 396/180 = 2.2 hours = 2 hours, 12 minutes (flight out)

Answer: 2.2 hours