Question

a plane left 30 minutes late tham its scheduled time and in order to reach the destination 1500 km away in time, it had speed by 100 km/hr from the usual speed. find its usual speed

Answer 1

Let the usual time taken by the aeroplane = x km/hr
Distance to the destination = 1500 km
Case (1)
Speed = Distance / Time
           = (1500 / x) hrs
Case (2)
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 not be negative,
The usual time taken by the aeroplane = 2 hrs
and the usual speed = (1500 / 2)
                                 = 750 km/hr.

Answer 2

The leaving time would 30min before!

So,
Distance = 1500km
Time = x
2nd time = x +30
The 1st speed = 100km/h

To find the 2nd speed I.e usual speed

Now,
S=D/T
100=1500/x
X = 1500/100 =15

So they reached at 15

So,
Usual speed =
S =D/T
S = 1500/x+30
S = 1500/15+30
S = 1500/45
S = 33.33km/h

So,
Usual speed = 33.33km/h

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