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An aeroplane lefts 30 minute later than it's shedule 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 time.

An aeroplane lefts 30 minute later than it's shedule 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 time.

Grade:12th Pass

1 Answers

Sudheesh Singanamalla
114 Points
10 years ago

Let the usual speed of the plane be 'x' hours

Time taken to cover 1500km with usual speed = 1500/x hrs

time taken to cover 1500km with speed of (x+250) = 1500/(x+250) hrs

1500/x = 1500/(x+250) + 1/2

1500/x - 1500/(x+250) = 1/2

1500x + 1500*250 - 1500x / (x*(x+250)) = 1/2

1500*250 / x2+250x = 1/2

750000 = x2 + 250x

x2+250x - 750000 = 0

x2 + 1000x - 750x - 750000 = 0

x ( x+1000) - 750 (x+1000) =0

(x+1000)(x-750) = 0

which means x = -1000 , which is not possible , as speed cannot be negative

or x = 750

so the usual speed of the plane is 750 kmph

usual time = distance / speed = 1500 / 750 = 150/75 = 2 hours !

 

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