Question

A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it increased the speed by 250 km/h from the usual speed. Its usual speed is

Answer 1

here is your answer

dear MaTe......

Answer 2

Let the usual speed of the aeroplane = x km/h

Then it's increased speed = (x+250)km/h

Time difference in the two cases = 30 min. = 1/2 hr.

$\sf\red{\frac{1500}{x} - \frac{1500}{x + 250} = \frac{1}{2} }$

$\longrightarrow$$\sf\red{2 \times 1500((x + 250) - x) = x(x + 250)}$

$\longrightarrow$$\sf\red{{x}^{2} + 250x - 750000 = 0}$

$\longrightarrow$$\sf\red{(x - 750)(x + 1000) = 0}$

$\longrightarrow$$\sf\red{x = 750 \: or \: x = - 1000}$

As the speed cannot be negative, x ≠ -1000 ,so x = 750

Hence, the usual speed of the aeroplane = 750km/h