Question

Two places A and B are 120km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 6 hours, and if they move in opposite directions, they meet in 1 hour 12 minutes. Find the speed of each car.

Answer 1

The speed of the first car is 60 km/h, and the speed of the second car is 10 km/h when they move in the same direction. When they move in opposite directions, the speed of the cars can be any value.

Step-by-step explanation:

Let's assume that the speed of the first car is x km/h and the speed of the second car is y km/h.

In the same direction:

When two objects are moving in the same direction, their relative speed will be the difference between their speeds. Since they meet in 6 hours, the distance traveled by the slower car (starting from B) must be 6 hours times its speed:

1. 
   
3. Distance traveled by the slower car = 6y km

Now, the distance between A and B is 120 km. So, the distance traveled by the faster car (starting from A) must be 120 km minus the distance traveled by the slower car:

1. 
   
3. Distance traveled by the faster car = 120 km - 6y km = 120 - 6y km

Since both cars meet at the same point in 6 hours:

1. 
   
3. Distance traveled by the slower car = Distance traveled by the faster car
4. 
   
6. 6y = 120 - 6y

We can rearrange the equation to solve for y:

1. 
   
3. 12y = 120
4. 
   
6. y = 10

Now, we can substitute the value of y back into one of the previous equations to find the value of x:

1. 
   
3. x = 120 - 6y = 120 - 6(10) = 120 - 60 = 60

In the same direction, the speed of the first car is 60 km/h and the speed of the second car is 10 km/h.

In opposite directions:

When two objects are moving in opposite directions, their relative speed will be the sum of their speeds. Since they meet in 1 hour and 12 minutes (equivalent to 1.2 hours), the distance traveled by the first car (starting from A) can be calculated:

1. 
   
3. Distance traveled by the first car = 1.2 times its speed = 1.2x km

The distance traveled by the second car (starting from B) is the same as the distance traveled by the first car:

1. 
   
3. Distance traveled by the second car = 1.2x km

Since both cars meet at the same point in 1 hour and 12 minutes:

1. 
   
3. Distance traveled by the first car = Distance traveled by the second car
4. 
   
6. 1.2x = 1.2x

Here, we can see that the equation is satisfied for any value of x. Therefore, there can be any speed for the cars when they move in the opposite direction.

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