Question

An aeroplane left 30 min later than its scheduled time and inorder to teach on time 1500 km away it increased its speed to 250 km/hr by its usual speed . Determine the usual speed​.

Answer 1

Answer:

Speed = 750 km/hr

Step-by-step explanation:

Let 's' be the usual speed to cover the distance of 1500 km

Then, time required = $\frac{1500}{s}$

If the plane left 30 minutes late, the time traveled = ($\frac{1500}{s}$ - $\frac{1}{2}$) hours

To cover the distance it increased its speed by 250km/hr so the new speed = (s + 250)

Since the distance covered is the same

($\frac{1500}{s}$ - $\frac{1}{2}$) * (s + 250) = 1500

⇒ 1500 + $\frac{1500 * 250}{s}$ - $\frac{s}{2}$ - 125 = 1500

⇒ $\frac{1500 * 250}{s}$ - $\frac{s}{2}$ - 125 = 0

Multiplying the equation with -2s

⇒ s² + 250s - (1500 * 250 * 2) = 0

⇒ s² + 1000s - 750s - (1500 * 250 * 2) = 0

⇒ (s + 1000) * (s - 750) = 0

⇒ s = -1000  OR  s = 750

Since speed cannot be negative s = 750