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 100 km/h from its usual speed.find its usual speed.

Answer 1

Let the usual time taken by the aeroplane = x km/hr
Distance to the destination = 1500 km

--------Speed = Distance / Time = (1500 / x) Hrs
 

------------Time taken by the aeroplane = (x - 1/2) Hrs
            Distance to the destination = 1500 km
Speed = Distance / Time = 1500 / (x - 1/2) Hrs
 
Increased speed = 100 km/hr
 
[1500 / (x - 1/2)] - [1500 / x] = 100
 150((10/x-1/2)-10/x0=100
 15 /x -1/2- 15/x =1 
30x -30x +15=2x^2-x
15=2x^2-x
2x^2-x-15=0
2x^2 - 6x+5x-15=0
2x(x-3)+5(x-3)
2x+5=0  or x-3 =0
x=-5/2   or x=3

Since, the time can not be negative,
The usual time taken by the aeroplane = 3hrs
and the usual speed = (1500 / 3) = 500km/hr

Answer 2

YOUR ANSWER IS IN THE ATTACHMENT GIVEN BELOW.

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The usual speed =500Km/h

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I hope it helps you

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