Question

a plane left 30 minutes late than a scheduled time and in order to reach the destination 1500 km away in time it had to increase the speed by 100 km per hour from the usual speed find its usual speed

Answer 1

Let speed=xkm
Time=distance/speed
30min to hours=3/6
1500/x-1500/x+100=3/6

1500(x+100)-1500x/x^2+100x=3/6
1500x+150000-1500x/x^2+100x=3/6
150000/x^2+100x=3/6
6(150000)=3(x^2+100x)
900000=3x^2+300x
3x^2+300x-900000=0
The equation formed:x^2+100x-300000
The solve by yrsel guys

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