Question

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time it had to increase its speed by hundred kilometre per hour from usual speed find its usual speed

Answer 1

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Syeda , SubjectMatterExpert

Member since Jan 25 2017

Answer,


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

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Answer 2

Let the usual speed of plane be 'S' km/hr.
Usual time = T.
It left 30 minutes late than usual:
Hence at normal speed, it would have reached half hour late:
1500/S = T + 30 mins = T + 1/2 hrs.....(i)

S = S + 100, reached on time
1500/S + 100 = T....(ii)
(i) - (ii)
1500/S - 1500/S+100 = 1/2
1500*(1/S - 1/S+100) = 1/2
1500*2*(S+100-S/(S*(S+100))) = 1
1500*2*100 = S*(S+100)
50*30*10*10*2 = S*(S+100)
50*10* 30*10*2 = S*(S+100)
500 * 600 = S*(S+100)
Comparing S = 500, then S+100 = 600
Hence, S = 500 km/hr
Usual speed = 500 km/hr
Hope it helps.