Question

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km / hr from its usual speed. Find the usual speed of the plane.

Answer 1

Time = distance/speed 

Given, plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km / hr from its usual speed. 

Let the usual speed be ‘a’.

\(\frac{1600}a{}-\frac{1600}{a\,+\,400}=\frac{40}{60}\)

⇒ 3(1600 × 400) = 2(a² + 400a)

⇒ a² + 400a – 960000 = 0

⇒ a² + 1200a – 800a – 960000 = 0 

⇒ a(a + 1200) – 800(a + 1200) = 0 

⇒ (a + 1200)(a – 800) = 0 

⇒ a = 800 km/hr