Question

A Plane left 30 minutes late than its scheduled time and in order to reach destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

Answer 1

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Answer 2

Let the speed of plane be x km/hr

Time taken to cover 1500 km

Time (1) $\bf\huge = \frac{Distance}{Speed}$

= $\bf\huge\frac{1500}{100}$

Time taken to cover 1500 km

When speed increased 100 km/hr

Time (2) = $\bf\huge\frac{1500}{p\:+\:100}$

According to the Question

Time (1) + Time (2) = 30 minutes = $\bf\huge\frac{1}{2} hr$

$\bf\huge\frac{1500}{p} - \frac{1500}{p\:+\:100} = \frac{1}{2} hr$

$\bf\huge\frac{1500p\:+\:1500\: -\:1500p}{p(p\:+\:100)} = \frac{1}{2} hr.$

$\bf\huge\frac{15000}{p^2 + 100p} = \frac{1}{2} hr.$

p^2 + 100p = 30000

p^2 + 100p - 30000 = 0

p^2 + 600p - 500p  - 3000 = 0

p(p + 600) - 500(p + 600) = 0

(p + 600)(p - 500) = 0

If p + 600 = 0

p  = - 600 speed can not be negative.

If  p - 500 = 0

p  = 500

Speed of the plane = 500 km/hr