**Two Cars Travelling in Opposite Directions :**

In this section, we will learn how to solve problems based on two cars travelling in opposite directions.

The relationship between distance, speed and time.

Time = Distance / Speed

Speed = Distance / Time

Distance = Time ⋅ Speed

To convert minutes into hour, we should divide the given minutes by 60.

- If we want to convert the speed from km/hr to m/sec, we should multiply the speed by 5/18.
- If we want to convert the speed from m/sec to km/hr, we should multiply the speed by 18/5.

**Example 1 :**

Town A and Town B are 420 km apart. A car leaves Town A for Town B and another car leaves Town B for Town A. If car A has a head start of 2.5 hours, the two cars will pass each other 2.5 hours after car B starts its journey. If car B has a head start of 2 hours, the two cars will pass each other 3 hours after car A starts its journey. Find their respective speeds.

**Solution :**

Let x and y be the speed of car A and car B respectively.

**What is head start ?**

When a runner allows to start the race 'x' meters ahead from the starting point , then we can say that the runner got a head start of (start up) x meters.

If the runner allows starting the race by 't' seconds earlier than the other runners, then the runner got a head start of t seconds.

Time taken by car A to meet car B is 5 hours. At the meeting point, car B has traveled 2.5 hours.

5x + 2.5y = 420 -------(1)

Time taken by car B to meet car A is 5 hours. At the meeting point, car B has traveled 5 hours and car A has traveled 3 hours.

3x + 5y = 420 -------(2)

(1) ⋅ 2 ==> 10x + 5y = 840 -----(3)

(3) - (2)

10x - 3x = 840 - 420

7x = 420

x = 420/7

x = 60

By applying the value of x in (2), we get

3(60) + 5y = 420

180 + 5y = 420

5y = 420 - 180

5y = 240

y = 48

The speed of car A and car B are 60 km/hr and 48 km/hr respectively.

- Find the time taken by the train to pass a man
- Find the time taken by a train to pass a bridge or tunnel
- Train passes a moving object in the same direction
- Problems on finding the length of the train
- Finding the average speed of the round trip
- Finding the Speed When the Distance Traveled is Same
- Two Cars Traveling Same Direction Different Speeds

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