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# A man takes 6 hours to travel 36 kilometres. How long will he take to travel 120 kilometres?

Last updated date: 02nd Aug 2024
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Hint: A man takes 6 hours to travel 36 kilometres. The distance travelled and the time taken is given, so using this distance and time calculate the speed of man. Speed will be the same and here the unit of speed is kilometres per hour. And then we have to find the time which will be taken by the man to travel 120 kilometres. Here we know the distance and speed, so using this calculate the time.
Formulas used:
Speed is the ratio of the distance travelled over the time taken, $S = \dfrac{d}{t}$
Time will be the ratio of distance over speed, $t = \dfrac{d}{S}$

We are given that a man takes 6 hours to travel 36 kilometres.
We have to calculate the time taken by the same man to travel 120 kilometres.
When the distance is 36 kilometres, time taken is 6 hours.
So the speed will be $S = \dfrac{d}{t}$
$\Rightarrow S = \dfrac{{36}}{6} \\ \Rightarrow S = 6km/hour \;$
When the distance is 120 kilometres, then the time taken by the man with a speed 6 km/ hour will be $t = \dfrac{d}{S}$
$\Rightarrow t = \dfrac{{120}}{6}hours \\ \Rightarrow t = 20hours \;$
Therefore, the man will take 20 hours to travel 120 kilometres with a speed 6 kilometres/ hour.
So, the correct answer is “20 hours”.

Note: Another approach
Time taken by the man to travel 36 kilometres is 6 hours.
So the time taken by the man to travel 1 km will be $\dfrac{6}{{36}} = \dfrac{1}{6}hours$
In the same way to travel 120 kilometres, the time taken by the man will be
$120 \times \dfrac{1}{6} = 20hours$
The man takes 20 hours to travel 120 kilometres.