Question

A private jet had been flying for 2 hours when it encountered strong head winds which reduced its speed by 40 miles per hour. If it took the plane 5 hours to travel 1,380 miles, find its speed before flying into the head winds.

Answer 1

Answer:

The speed before flying into the head winds was 79.2 mph.

Step-by-step explanation:

These measures can be related the following way:

$v = \frac{s}{t}$

In which v is the speed, s is the distance and t is the time.

If it took the plane 5 hours to travel 1,380 miles.

This means that the AVERAGE speed was:

$v = \frac{1380}{5} = 276$ mph

There are two intervals(First two hours, last three hours).

The first two hours have an average speed of a, and the last three hours have an average speed of b = a-40.

276 is the weighed average. So:

$\frac{2a + 3b}{5} = 276$

$2a + 3b = 276$

$2a + 3(a - 40) = 276$

$5a - 120 = 276$

$a = 79.2$ mph

The speed before flying into the head winds was 79.2 mph.

Answer 2

Answer:

300 mph

Step-by-step explanation:

Let s represent the initial speed of the plane in miles per hour. Then s-40 is the reduced speed after encountering the head wind. The time spent flying against the head wind was 5 - 2 = 3 hours.

... distance = speed×time

... 1380 = s×2 + (s -40)×3

... 1380 = 5s -120 . . . . . . . . . eliminate parenthses

... 1500 = 5s . . . . . . . . . . . . . add 120

... 300 = s . . . . . . . . . . . . . . . divide by 5