Question

A plane left 30 minutes late than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/h from its usual speed.find its usual speed

Answer 1

Given
Distance =1500km
Left 30min late
Speed Increase by 250km/h

Let usual speed=x

Time =distance /speed

=1500/x

Now speed in increased by 250km/hr

New speed =(x+250)

Then
Time =1500/(x+250)

So we can write

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

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

$\frac{375000}{x(x + 250)} = \frac{1}{2}$

X²+250x-750000=0

Now find two numbers who's sum=+250 and multiple =-750000

1000,-750

X²+1000x-750x-750000

X(x+1000)-750(x+1000)

(x+1000)(x-750)

X+1000=0

X=-1000

Speed can't be in negative

X-750=0

X=750km/h

Usual speed =750km/h

This is ur ans hope it will help you in case of any doubt comment below

Answer 2

Hope it helps ....regards SR