# A man covers a distance of 200 km travelling with a uniform speed of x km/hr.The distance could have been covered in 2hrs less,had the speed been (x+5)km/hr.Calculate the value of x. quadratic equation

2
by singhsumita40

2014-12-19T10:54:04+05:30
Speed of man = x km/hr
Distance = 200 km
Therefore, time = 200/x hrs
In the second case,
Speed = (x + 5) km/hr
Therefore, time = 200/(x + 5) hrs
According to the condition,
200/x - 200/(x + 5) = 2
=> 200[1/x - 1/(x + 5)] = 2
=> 200[(x + 5 - x) / x(x + 5)] = 2
=> (200 × 5) / (x² + 5x) = 2
=> 1000 = 2x² + 10x
=> 2x² + 10x - 1000 = 0
=> x² + 5x - 500 = 0  (Dividing by 2)
=> x² + 25x - 20x - 500 = 0
=> x(x + 25) -20(x + 25) = 0
=> (x + 25)(x-20) = 0
Either (x + 25) = 0, then x = -60, but it is not possible as speed can't be negative
or (x - 20) = 0, then x = 20 Ans.

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2014-12-19T14:31:59+05:30
The time taken for 200km at rate of x km/hr
200/x hrs
Time to cover 200km at rate of x+5 km/hr
200/(x+5)  hrs
ATQ we have        200/x= 200/(x+5) +2
⇒  200(x + 5)= x(200+2x+10)
⇒ 200x +1000 = 210x + 2x²
⇒ x²+5x -500=0