A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500Km away in - Maths - Quadratic Equations

Question

A plane left 30 minutes later than the scheduled time and in
order to reach its destination 1500Km away in time it has to
increase its speed by 250 Km/hr from its usual speed Find its usual
speed

Ankush Jain · Accepted Answer

Let the usual speed of the plane be x km/hr.

Increased speed of the plane = (x + 250) km/hr

Time taken to reach the destination at usual speed, $t_{1} = \frac{1500}{x} hr$

Time taken to reach the destination at increased speed, $t_{2} = \frac{1500}{x + 250} hr$

Given, t₁ – t₂ = 30 min

$∴ \frac{1500}{x} hr - \frac{1500}{x + 250} hr = \frac{30}{60} hr \Rightarrow \frac{1500 x + 375000 - ` 1500 x}{x (x + 250)} = \frac{1}{2} \Rightarrow x^{2} + 250 x = 750000 \Rightarrow x^{2} + 250 x - 750000 = 0 \Rightarrow x^{2} + 1000 x - 750 x - 750000 = 0 \Rightarrow x (x + 1000) - 750 (x + 1000) = 0 \Rightarrow (x + 1000) (x - 750) = 0 \Rightarrow x + 1000 = 0 or x - 750 = 0 \Rightarrow x = - 1000 or x = 750 ∴ x = 750 (∵ Speed cannot be negative)$

Thus, the usual speed of the plane is 750 km/hr.

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500Km away in time it has to increase its speed by 250 Km/hr from its usual speed. Find its usual speed.