1. ## Plane distance problem

An airplane was supposed to cover the distance of 2900 km. However, after covering 1700 km, it had to land and wait on the ground for 1 hours and 30 minutes. After it took off again, its average speed was 50 km/h less than before. Find the original average speed of the plane if it is known that it completed the flight five hours after departure. help would be appreciated thanks!

2. Hello, jarny!

An airplane was supposed to cover the distance of 2900 km.
However, after covering 1700 km, it had to land and wait on the ground for 1 hours and 30 minutes.
After it took off again, its average speed was 50 km/h less than before.
Find the original average speed of the plane if it completed the flight 5 hours after departure.

Let x = original speed of the plane (km/hr).

It flew 1700 km at x km/hr.
. . This took: .1700/x hours.

It flew the remaining 1200 km at (x - 50) km/hr.
. . This took: .1200/(x - 50) hours.

The plane flew a total of 3½ hours.

. . And there is our equation: .1700/x + 1200/(x - 50) .= .7/2

Multiply through by 2x(x - 50): .3400(x - 50) + 2400x .= .7x(x - 50)

This simplifes to the quadratic: .7x² - 6150x + 170,000 .= .0

. . which factors: .(x - 850)(7x - 200) .= .0

. . and has roots: .x .= /850, 200/7

We reject the smaller root: x = 200/7
At about 28.6 km/hr, it would take over 100 hours to fly 2900 km.

Therefore, the original speed of the plane was: 850 km/hr.