Question

a plane left 30 minutes late that its schedule 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 speed of plane be x km/h

Let convert time 30min in hour

=30/60 =1/2

According to question:

1500/x-1500/x+100=1/2

(1500x-1500x+150000)/x^2+100x=1/2

150000×2=x^2+100x

X^2+100x-300000=0

X^2+600x-500x-300000=0

X(x+600)-500(x+600)

(X-500) (x+600)

X=500. X=-600;

But Speed can never be negative

X=500km/h

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