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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 on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.
Solution
Let the usual speed of the plane be x km/hr
And the new speed of the plane after increased by 250 is `(x + 250)` km/hr
According to question
`1500/x - 1500/((x + 250)) = 30/60`
⇒ `(1500x + 1500 xx 250 - 1500x)/(x(x + 250)) = 1/2`
⇒ `1500 xx 250 xx 2 = x(x + 250)`
⇒ `750000 = x^2 + 250x`
⇒ `x^2 + 1000x - 750x - 750000 = 0`
⇒ `(x + 1000)(x - 750) = 0`
x = 750, - 1000
Speed can not be negative so -1000 will be neglected
Therefore, usual speed of the plane is 750 km/hr.
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