## TWO CARS TRAVELING SAME DIRECTION DIFFERENT SPEEDS

Two Cars Traveling Same Direction Different Speeds :

In this section, we will see the problems based on two cars traveling in the same direction but in different speeds.

Example 1 :

Two cars traveling at 62 km/hr and 54 km/hr respectively, left Town A for Town B at the same time. The faster car passed on oncoming truck 10 hours later. An hour after that, the slower car and the truck also passed each other. Find the speed of the truck.

Solution :

Both Car A and car B meets the truck.

Car A meets the truck in 10 hours. Car B meets the truck in 11 hours.

Distance traveled by the car A in 10 hours  =  62 (10)

=  620 km

Distance traveled by the car B in 10 hours  =  54 (10)

=  540 km

At that time when car A meets the truck, car B will be at 80 km away from both car A and truck.

In order to meet both car B and truck, they will together travel 80 km. Time taken is 1 hour.

Let x be the speed of the truck.Since they are travelling in the opposite direction, the relative speed will be 54 + x.

1  =  80 / (54 + x)

54 + x  =  80

x  =  80 - 54

x  =  26

Hence the speed of the truck is 26 km/hr.

Example 2 :

A backpacker was walking at a speed of 5 km/hr towards Mississauga that was 40 km away. He got a ride from a motorist who drove at 25 km/hr in the same direction. They arrived at Mississauga 2.5 hours later. How far had the backpacker walked before he took a ride from the motorist ?

Solution :

A backpacker was walking at the speed of 5 km/hr towards the destination which is 40 km away from the starting point.

After some time, he is getting the bike ride with the speed of 25 km/hr. After taking 2.5 hours he reaches the destination.

Let x be the distance covered before he got bike drive.

Time  =  Distance / Speed

2.5  =  (x/5) + (40 - x)/25

2.5  =  (5x + 40 - x)/25

2.5  =  (4x + 40)/25

62.5  =  4x + 40

4x  =  62.5 - 40

4x  =  22.5

x  =  5.625 km

Hence the distance covered before the bike ride is 5.625 km.

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