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 his speed by 100 km per hour from the usual speed find its usual speed

Answer 1

let the usual speed of the plane be x km/hrs.

Then according to the condition

x+ 100 = 1500/0.5 km/hr

=>x + 100 = 3000 km/hr

So x = 2900 km/hr

Answer 2

Solution :-

Let the original speed of train be x km/hr

New speed = (x + 100) km/hr

We know that,

Time = Distance / Speed

Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.

According to the question,

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

=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2

=> 2(15000) = x(x + 100)

=> 30000 = x² + 100x

=> x² + 100x - 30000 = 0

=> x² + 600x - 500x - 30000 = 0

=> x(x + 600) - 500(x + 600) = 0

=> (x - 500) (x + 600) = 0

=> x = 500 or x = - 600

∴ x ≠ - 600 (Because speed can't be negative)

Hence,

Its usual speed = 500 km/hr