Question

In a flight of 3000 km an aircraft was slowed down by bad weather. If average speed for the trip was reduced by 100 km/h and the time increased by one hour, the original duration of the flight is

Answer 1

Answer:

Step-by-step explanation:

Let the usual speed of the aircraft be 'x' km/hr

So, the reduced speed will be (x - 100) km/hr

Time taken to reach the destination at usual speed

T1 = (3000/x) hr

Time taken to reach the destination at reduced speed 

T2 = (3000/x-100) hr

Given : T2 - T1 = 1 hr

∴ (3000/x-100) hr - (3000/x) hr = 1 hr

⇒ (3000x - 3000x + 300000)/(x)(x-100) = 1 hr

⇒ x² - 100x - 300000 = 0

⇒ x² - 600x + 500x - 300000 = 0

⇒ x(x - 600) + 500(x - 600) = 0

⇒ (x - 600)(x + 500) = 0

⇒ x = 600 or x = - 500

Speed cannot be negative. Hence x = 600 km/hr is correct speed.

Therefore the duration is 3000/x= 3000/600= 5 hours