Question

A train travels a distance of 180 km at a uniform speed if the speed had been 9 km/h more than it would take one hour less to cover the same distance find the speed of the train

Answer 1

Answer:

36km/h.

Step-by-step explanation:

Let the speed of train be x km /h

Distance = 180 km

So, time = 180 / x

When speed is 9 km/h more, time taken = 180 / x+9

According to the given information:

180 / x - 180 / x+9 = 1

180 (x+9-x) / x(x+9) = 1

180 * 9 = x(x+9)

1620 = x2 + 9x

x2 + 9x - 1620 = 0

x2 + 45x - 36x - 1620 = 0

x(x+45) - 36(x+45) = 0

(x-36)(x+45) = 0

x = 36 or -45

But x being speed cannot be negative.

So, x = 36

Hence, the speed of the train is 36km/h.

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Answer 2

$\Large{\underline{\underline{\tt{\red{Given}}}}}$

A train travels a distance of 180 km at a uniform speed if the speed had been 9 km/h more than it would take one hour less to cover the same distance

$\Large{\underline{\underline{\tt{\red{Find\:out}}}}}$

Find the speed of the train

$\Large{\underline{\underline{\tt{\red{Solution}}}}}$

★Let the speed of train be x

As we know that

(★) Time = distance/speed

• Distance travelled by train = 180km
• Time taken = 180/x

*According to the given condition*

If the speed had been 9 km/h more than it would take one hour less to cover the same distance.

$\implies\tt \dfrac{180}{x}-\dfrac{180}{x+9}=1 \\ \\ \\ \implies\tt \dfrac{180(x+9)-180x}{x(x+9)} = 1 \\ \\ \\ \implies\tt \dfrac{180x + 1620 - 180x}{x^2+9x}=1 \\ \\ \\ \implies\tt \dfrac{1620}{x^2+9x}=1 \\ \\ \\ \implies\tt x^2+9x=1620 \\ \\ \bf{\underline{\blue{Splitting\: middle\: term}}} \\ \\ \implies\tt x^2+9x-1620=0 \\ \\ \\ \implies\tt x^2+45x-36x-1620=0 \\ \\ \\ \implies\tt x(x + 45)-36(x+45)=0 \\ \\ \\ \implies\tt (x+45)(x-36)=0$

Either

➞ (x + 45) = 0

➞ x = - 45

Or

➞ (x - 36) = 0

➞ x = 36

NOTE : ★$\sf{\underline{\orange{Speed\:never\:in\: negative}}}$★

Hence, speed of the train is 36km/h