1.

A plane left 30 minutes late than its scheduled time and in order to reach the destination1500 km away in time, it had to increase the speed by 250 km/h from the usual speed.Find its usual speed.

Answer» Let the usual speed = x km/hr
and distance travelled = 1500 km
`therefore` time taken in usual speed = `(1500)/(x)` hr
Increased speed = (x + 250) km/hr
`therefore` time taken in increased speed = `(1500)/(x + 250)` hr
But difference in both timings = 30 min = `(1)/(2)` hr
`implies (1500)/(x) - (1500)/(x + 250) = (1)/(2)`
implies` 1500 [(x + 250 - x)/(x(x + 250))] = (1)/(2)`
implies x(x + 250) = 500 `xx` 1500
implies `x^(2) + 250x - 750000 = 0`
implies (x + 1000)(x - 750) = 0
`therefore x = 750` or x = - 1000
But speed cannot be negative.
Hence, the usual speed = 750 km/hr.


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