Question

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

Answer 1

Let the usual speed of the plane = x km/hr

Increased speed of the plane = (x + 100) km/hr

Time take to reach the destination at the usual speed, `t_1 = 1500/x` hr

Time take to reach the destination at the increased speed, `t_2 = 1500/(x + 100) hr`

Difference of both the times = t₁ - t₂ = 30 mins = `1/2` hr

`1500/x - 1500/(x + 100) = 1/2`

`=> 1500 (x + 100) - 1500x = (x(x + 100))/2`

`=> 1500x + 150000 - 1500x = (x(x+100))/2`

`=> 300000 = x^2 +  100x`

`=> x^2 + 100x - 300000 = 0`

`=> x^2 + 600x - 500x - 300000 = 0`

`=> (x + 600) (x - 500)  = 0`

x = 500 or x = -600

As speed cannot be negative so x = 500 km/hr.

Hence, the usual speed of the plane is 500 km/hr