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

let x=usual speed of plane
x+250=increased speed of plane
30 min=1/2 hr
travel time=distance/speed
...

lcd:x(x+250)
1500(x+250)-1500x=x(x+250)/2
1500x+375000-1500x=x^2+250x/2
750000=x^2+250x
x^2+250x-750000=0
(x+1000)(x-750)=0
x=750
usual speed of plane=750 km/hr


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Answer 2

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

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