Question

In 3hours, a train covers 195 km. travelling at the same speed, what distance would the train cover in 5 hours.

Answer 1

Hint: The given problem is based on the concept of physical quantity called speed and we know that the relation between speed time and distance is given by \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\] . Since the train is travelling at the same speed we can also solve this using a unitary method . That is, we find how many kilometers a train covers in one hour. Then we can find it for 5 hours. Now we solve this using the relation between speed, time and distance.

Complete step by step solution:
Let us solve the given problem by considering two cases as follows:
Case (1): given data: In 3hours, a train covers 195 km
 \[ \Rightarrow \] Time= \[{t_1}\]=3hours
 \[ \Rightarrow \]distance= \[{d_1}\]=195km
Let \[{s_1}\]be the speed of the train in case 1
By using above formula, we can write \[{s_1}\] =\[\dfrac{{{d_1}}}{{{t_1}}}\]
Case (2): given data:
 \[ \Rightarrow \] Time= \[{t_2}\]=5hours
 \[ \Rightarrow \]distance= \[{d_2}\]=?
Let \[{s_2}\]be the speed of the train in case 2
By using above formula, we can write \[{s_2}\] =\[\dfrac{{{d_2}}}{{{t_2}}}\]
Now in the question clearly given that speed is same in both the cases that is \[{s_1}\]= \[{s_2}\]
\[ \Rightarrow \dfrac{{{d_1}}}{{{t_1}}} = \dfrac{{{d_2}}}{{{t_2}}}\]
Since \[{d_2}\]is unknown we have to find the value of \[{d_2}\]so keeping \[{d_2}\]as it is and substituting the remaining values in above equation, we get
\[ \Rightarrow \dfrac{{195}}{3} = \dfrac{{{d_2}}}{5}\]
On simplification we get
\[ \Rightarrow \dfrac{{195 \times 5}}{3} = {d_2}\]
\[ \Rightarrow \dfrac{{975}}{3} = {d_2}\]
\[ \Rightarrow {d_2} = 325\]km
Therefore, by travelling at the same speed the train will cover a distance of \[325km\]
So, the correct answer is 325 Km”.

Note: We can solve this by unitary method.
We know that in 3 hours, the train covers 195 km.
Then in one hour the train covers
\[ \Rightarrow \dfrac{{195}}{3}km\]
\[ \Rightarrow 65km\]
That is, a train covers 65km in an hour.
Since the train is traveling with same speed , then in 5 hours the train covers
\[ \Rightarrow 5 \times 65km\]
\[ \Rightarrow 325km\]
In both cases we have the same answer.