Question

a plane averaged 400 mph on a trip going east, but only 280 mph on the return trip. The total flying time in both directions was 8.5 hours. what was the one-way distance?

Answer 1

Answer:

1400 miles

Step-by-step explanation:

Speed is the time rate of change of distance. It is the ratio of distance to time and is given by the equation:

$Speed(S) = \frac{distance(d)}{time(t)}\\ S=\frac{d}{t}$

plane averaged 400 mph on a trip going east, but only 280 mph on the return trip.

The time spent (t₁) in going east is given by:

$S=\frac{d}{t_1}\\ t_1=\frac{d}{S} =\frac{d}{400mph}$

The time spent (t₂) in going east is given by:

$S=\frac{d}{t_2}\\ t_2=\frac{d}{S} =\frac{d}{280mph}$

The total time (t) = t₁ + t₂

t = t₁ + t₂ = 8.5 hours

$\frac{d}{400}+\frac{d}{280} =8.5\\280d+400d=952000\\680d=952000\\d=1400miles$

Therefore the one way distance is 1400 miles