Question

A plane left 30minutes later from its scheduled time.in order to reach its destination 1500 km away on time ,it has to increase it's speed 250km/hr from its usual speed .find its usual speed.

Answer 1

let the usual speed be x km/hr
actual speed=(x+250) km/hr
time taken at usual speed= (1500/x)km
time taken at actual speed=(1500/x+250) km
differencevbetween tue two time taken = 1/2 hr
1500/x-1500/x+250=1/2
1/x-1/x+250=1/3000
250/x^2+250x=1/300
x^2+250x-750000=0
x^2+1000x-750x-750000=0
x(x+1000)-750(x+1000)=0
x+1000 =0 or x-750=0
x=-1000 or x= 750
x=750 [because speed cannot be in negative]

Answer 2

Solution :-

Let the original speed of train be x km/hr
New speed = (x + 250) 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 + 250) = 1/2
=> (1500x + 37500 - 1500x)/x(x + 250) = 1/2
=> 2(37500) = x(x + 250)
=> 75000 = x² + 250x
=> x² + 250x - 75000 = 0
=> x² + 1000x - 750x - 75000 = 0
=> x(x + 1000) - 750(x + 1000) = 0
=> (x - 750) (x + 1000) = 0
=> x = 750 or x = - 1000

∴ x ≠ - 1000 (Because speed can't be negative)


Hence,
Its usual speed = 750 km/hr