Question

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

Answer 1

⭐hey there!!

=>Let the usual time taken by the aeroplane = x km/hr

Distance to the destination = 1500 km

Casual speed:

Casual Speed = Distance / Time = (1500 / x) Hrs

Hence it leave 30 min latter so convert 30 min into hr i.e 1/2 hr.

Time taken by the aeroplane = (x - 1/2) Hrs

Distance to the destination = 1500 km

Speed = Distance / Time = 1500 / (x - 1/2) Hrs

Increased speed = 250 km/hr

=> [1500 / (x - 1/2)] - [1500 / x] = 250

=> 1/(2x2 - x) = 1/6

=> 2x2 - x = 6

=> (x - 2)(2x + 3) = 0

=> x = 2 or -3/2

# the time can't be negative,
Then the usual time taken by the aeroplane = 2 hrs

So, usual speed = (1500 / 2) = 750 km/hr.
_______________________________________
⭐hope it will help u

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