Question

The distance between the two cities A and B is 330 km. A train starts from A at 8 am and travels towards B at 60 km/hr. Another train starts from B to 9 am and travels towards A at 75 km/hr. At what time do they meet?
(a) 10 am
(b) 10:30 am
(c) 11 am
(d) 11:30 am

Answer 1

Hint: We have two trains travelling towards each other from A and B. We will assume that these 2 trains meet after x hour from 9 am. Now we get that train from end A to travel from (x + 1) hour as it started at 8 am. So, using \[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}},\] we will find the distance travelled by the first train. Then using the same formula we will find the distance travelled by the second train. As the total distance is 330 km, so we will add these two distances to find the value of x.

Complete step-by-step answer:
We are given that two points A and B are 330 km apart. One train starts from A at 60 km/hr at 8 am while one train starts from B at 7 km/hr at 9 am in the direction of B and A respectively. We have to find the time at which these two will meet. Let us assume that they will meet x hours after 9 am. Now, the total distance between A and B is given as 330 km. We will find the distance travelled by each train. We know that the speed is given as \[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}.\]
We have the speed of the train starting from A is 60 km/hr. It started at 8 am. So, it will travel for (x + 1) hour. They meet at x hour after 9 am. So, applying the formula of speed, we get,
\[\Rightarrow 60=\dfrac{\text{Distance travelled by first train}}{x+1}\]
\[\Rightarrow \text{Distance travelled by first train}=60\left( x+1 \right)......\left( i \right)\]
Similarly, we use the speed formula to find the distance travelled by the other train. The speed of the other train is 75 km/hr and it travelled just for x hour. So, we get,
\[\Rightarrow 75=\dfrac{\text{Distance travelled by second train}}{x}\]
\[\Rightarrow \text{Distance travelled by second train}=75x......\left( ii \right)\]
As we know that the total distance is 330 km, we get,
Distance travelled by the first train – Distance travelled by second train = 330
Using (i) and (ii), we get,
\[\Rightarrow 60\left( x+1 \right)+75x=330\]
Simplifying, we get,
\[\Rightarrow 60x+60+75x=330\]
Solving for x, we get,
\[\Rightarrow 135x=270\]
\[\Rightarrow x=\dfrac{270}{135}\]
\[\Rightarrow x=2\]
Therefore, both trains meet 2 hours after 9 am, i.e. at 11 am.

So, the correct answer is “Option C”.

Note: For the first train, the time of meeting was (x + 1) hour or the first train travel for (x + 1) hour. Because we have that from 9 am the train meets after x hour. So, from 8 am, 1 hour is used to move up to 9 am and then x hour is used to meet. Remember 60 (x + 1) is not equal to 60x + 1. Whenever we multiply a number with the bracket, it is multiplied with each element of the bracket that lies inside, i.e. 60 (x + 1) = 60x + 60.