Question

a plane left 30 minuites latethan its scheduled timeand in orden to reach the destiriation 1500km away in time,it had to increase its speed by 100km/hr from the usual speed find its usual speed

Answer 1

original speed =1500/x
according to conditions =1500/x+250
time=1/2
1500/x-1500/x+250=1/2
1500(x+250)-1500x/x2+250x=1/2
350000/x2+250x=1/2
750000=x2+250
x2+250x-750000=0
(x+1000)*(x-750)=0
x=-1000,x=750
750km/hrs

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