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A Plane Left 30 Minutes Later than the Schedule Time and in Order to Reach Its Destination 1500 Km Away in Time, It Has to Increase Its Speed by 250 Km/Hr from Its Usual Speed. Find Its Usual Speed. - Mathematics

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Question

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

Solution

Let the usual speed of plane be x km/hr

Distance = 1500 km

From the given information we have

1500/x - 1500/(x + 250) = 30/60

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

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

x^2 + 250x - 750000 = 0

x^2 + 1000x - 750x - 750000 = 0

(x +  1000)(x - 750) = 0

x = -1000, 750

Since speed cannnot be negative So x = 750

Hence the usual speed of plane is 750 km/hr

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