What Are the Speeds of Two Cars Meeting on a Highway?

[ajay.05]

Homework Statement

Places A and B are 100 km apart on a highway. One car starts from A and the other from B, at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in hour. What are the speeds of two cars?

Homework Equations

http://sketchtoy.com/63036238

The Attempt at a Solution

In the first case,
I assumed that both are traveling toward a point C, and the speeds are x,y respectively(x>y).
Therefore, If car 2 were made to be still, then car 1 will travel with a speed of x-y
So, x-y=20 (Speed = Distance/time)

How can I continue with Case 2?
Help me out:)

 

[BvU]

Hello Ajay, and welcome to PF.

I liked the sketchtoy. But what you really need are some relevant equations.

For the first case:
One for the position of car A as a function of time, and one for the position of car B. Position of point C is where the cars are at the same place. Where that is is not relevant. But you know that at time t=5 hours the equality holds.

Second case same story, different expression for one of the two positions, different C (again, irrelevant). But at time t = 1 hour the equality holds.

And now you have two equations with two unknowns, the speeds of the cars. Presto, physics = math !

 

[NascentOxygen]

I would keep to the standard approach.

When traveling in the same direction, the distance each covers is its speed x duration. That gives you one equation.

What traveling in opposite directions, the distance each covers is its speed x duration. The other equation.

Two equations, two unknowns.

 

[BvU]

I assumed that both are traveling toward a point C

is a good start. You don't know the speeds, so you name them v_a and v_b. Position in one dimension can be given as x. And a reference point can be x_A=0, so that x_B=100 km.

So, starting from your relevant equation x(t) = x(0) + v * t

-- this is how you can write your Speed = Distance/time in a convenient way for later use ! --
(this way it has the look of an equation, as opposed to "conversation" )​

you write down the position of car a as a function of time:

x_a(t) = ...​

 

[tjmiller88]

Hi Ajay,

I would start by adding some additional detail to your sketch. Draw out each situation on an X-axis with some labels for your distance, and vector arrows labeled with the velocities v_a and v_b.

Then work on creating the position equations for each car in each situation, as BvU suggested.