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.
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.
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.
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