## TWO CARS TRAVELLING IN OPPOSITE DIRECTIONS

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.

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.

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