Q34 of 168 Page 7

An aeroplane left 30 minutes later than its scheduled time and in order to reach its destination 1500 km away in time, it had to increase its speed by 250 km/hr from its usual speed. Determine its usual speed.

Let the usual speed be x km /hr.


Actual speed = (x + 250) km/hr.


Time taken at actual speed = () hr.


Difference between the two times taken = hr.


Speed at that time = (x + 250) km/hr





Then, According to the question,





3000{250} = x2 + 250


0 = x2 + 250x – 750000


0 = x2 + (1000–750)x – 750000


0 = x2 + 1000x – 750x – 750000


0 = x(x + 1000) – 750(x + 1000)


0 = (x + 1000) (x – 750)


x = –1000 or x = 750


Usual speed = x = 750 km /hr


⇒ x = 750 【 speed cannot be negative】


Hence , the usual speed of the aeroplane was 750 km / hr.


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