Question

A train is moving with a uniform speed of 120 km per hour.
(i). How far will it travel in 36 minutes?
(ii). In how much time will it cover 210 km?

Answer 1

Hint: To solve this type of questions we go for the relation of speed, distance and time which is given as, \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]. After making necessary substitutions we can easily calculate the result.

Complete step-by-step answer:
Given that the train moving with speed 120 km per hour. We have to find out the distance it will cover in 36 minutes and also the time it will take to cover a distance 210 km.
We know the speed, time and distance relation as,
\[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]
(i)Given, Speed S = 120 km per hour and time T = 36 minutes
Now because we have a unit of speed as km/hour so we will convert given time in hours.
We know there are 60 minutes in one hour,
Therefore,1 hour = 60 minutes.
Reversing the sides of the above equation we have,
60 minutes = 1 hour.
Therefore, \[36\text{ }minutes\text{ }=\dfrac{1}{60}(36)~=\text{ }0.6\text{ }hours\]
Now putting the values of speed and time in the formula,
\[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]
\[\begin{align}
  & \Rightarrow 120=\dfrac{\text{distance}}{0.6} \\
 & \Rightarrow \text{distance = (120)(0}\text{.6)} \\
 & \Rightarrow \text{distance = 72km} \\
\end{align}\]
Hence, the distance covered in 0.6 hours, that is, in 36 minutes is 72 km.

(ii)Given, speed = 120 km per hour. We have to calculate the time it will take to cover a distance 210 km.
Above implies Distance = 210 km
Now putting the values of speed and distance in the formula,
\[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]
We have,
\[\begin{align}
  & \Rightarrow 120=\dfrac{210}{time} \\
 & \Rightarrow time\text{ = }\dfrac{210}{120} \\
 & \Rightarrow time\text{ = 1}\text{.75 hr} \\
\end{align}\]
Hence, to cover a distance of 210 km with a speed of 120 km per hour, 1.75 hours is taken.

Note: The possibility or error in the question is using different units for different given values of variables. For instance, in this question we had to convert the given time into hours which is important because the speed is given in terms km/hour.
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