A train travels a distance of 480 km at a uniform speed. If the speed

Leave a Comment / NCERT book maths class 10th, quadratic / By preeti

(Q) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km / h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Ans: Let’s the speed of the train be $x$ km /h

We know that the time taken = $\frac{Distance}{Speed}$

Since the distance is 480 km, hence the time = $\frac{480}{x}$

In 2nd case, speed will be $x - 8$ km / h and the time taken to cover same distance of 480 km will be $\frac{480}{x - 8}$

By given condition, in 2nd case, time taken is 3 hrs more i.e.

Time taken in 2nd case = Time taken in 1st case + 3

$\Rightarrow \frac{480}{x - 8} = \frac{480}{x} + 3$

$\Rightarrow \frac{480}{x - 8} - \frac{480}{x} = 3$

$\Rightarrow \frac{480 x - 480 (x - 8)}{x(x - 8)} = 3$

$\Rightarrow (480) \frac{ x - (x - 8)}{x(x - 8)} = 3$

$\Rightarrow (480) \frac{ x - x + 8}{x(x - 8)} = 3$

$\Rightarrow (480) \frac{8}{x(x - 8)} = 3$

$\Rightarrow (480) \frac{8}{3} = x(x - 8)$

$\Rightarrow 1280 = x(x - 8)$

$\Rightarrow x^2 - 8 x - 1280 = 0$

$\Rightarrow x^2 - 40 x + 32 x - 1280 = 0$

$\Rightarrow x(x - 40) + 32 (x - 40) = 0$

$\Rightarrow (x - 40) (x + 32) = 0$

$\Rightarrow x = 40 ~ and ~ x = - 32$

Here, we reject x = – 32 because the value of the train’s speed can not be a negative number.

Therefore, speed of the train x = 40 km/ h

Hence, the speed of the train is 40 km/ h.

Check:

If train speed is 40 km/h, time taken to cover 480 kms = $\frac{480}{40}$ = 12 hrs

In 2nd case, speed is 8 km/h less, i.e. 40 – 8 = 32 km/h

Hence time taken to cover 480 kms = $\frac{480}{32}$ = 15 hrs

Since, time in 2nd case is 3 hrs more than the 1st one – it meets the given condition, hence our answer is correct.

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