Question

In a flight of $6000$$km$, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $400km/hour$ and time increased by $30$ minutes. Find the original duration of the flight.

Answer 1

In a flight of 6000 km, an aircraft was slowed down due to bad weather.
Its average speed for the trip was reduced by 400km/h and the time increased by 30 min.
Find the original duration of the flight
:
The weather has to be really bad to slow the plane down 400 km/hr, anyway:
:
Let s = original effective speed
then
(s-400) = speed in bad weather
:
Write a time equation; time = dist/speed
Bad weather time - normal time = 1/2 hr
- = .5
multiply by s(s-400) to clear the denominators; results:

6000s - 6000(s-400) = .5s(s-400)
6000s - 6000s + 2400000 = .5s^2 - 200s
A quadratic equation
.5s^2 - 200s - 2400000
solve this using the quadratic formula
You should get a positive solution of:
s = 2400 km/hr is the normal speed
:
Find the duration of the flight
6000/2400 = 2.5 hrs
Check this by finding the duration when speed reduced by 400 km/hr
6000/2000 = 3 hrs, a half hour longer