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Question
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.
Solution
Let the usual speed of plane be x km/hr
Total distance = 1500 km
From the given information, we have
`1500/x - 1500/(x + 250) = 30/60 = 1/2`
`(1500x + 1500 xx 250 - 1500x)/(x(x + 250)) = 1/2`
`(375000)/(x^2 + 250x) = 1/2`
x2 + 250x = 750000
x2 + 250x – 750000 = 0
x2 + 1000x – 750x – 750000 = 0
x(x + 1000) – 750(x + 1000) = 0
(x + 1000)(x – 750) = 0
x = –1000, 750
Since, speed cannot be negative.
So, x = 750.
Hence, the usual speed of plane is 750 km/hr.
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