When and where will two bikers meet?

[seanspan]

Homework Statement

There are two towns that are 20km apart. A biker leaves town#1 traveling at 20km/h and at the same time another biker leaves town#2 traveling at 15km/h. Where and when will they meet?
Given
d=20km between 2 towns
V biker 1=20km/h
V biker 2=15km/h

Homework Equations

d=v1t+1/2at^

The Attempt at a Solution

I know that you have to somehow make two equations and make them equal to each other and then solve for d and sub it into one of the equations to solve for t but I am having trouble starting please help

 

[Keldon7]

Think of what will be equal for both bikers when they meet. Is the distance they've traveled the same? The time perhaps?

 

[seanspan]

well the time will be equal i know that I am just having trouble with how to set it up. I assume you have to make 2 equations and then make them equal to each other I am just not sure what the equations should be.

 

[hotvette]

Correct, you'll have two equations that you'll need to equate. But, the applicable equation really should be the general form d = d₀ + v₀t + 1/2at² where d₀ represents the initial distance (i.e. postion) at t=0 with respect to a chosen coordinate system/origin. For example, if you choose the origin to be the initial starting point of the 1st biker, then d₀ = 0 for the 1st biker. Using the same origin, think about what d₀ would be for the 2nd biker and what happens over time. In the end, you want to find the time at which both bikers are in the same position (with respect to the same orgin), and from that you can find the location. When you write the equations, be careful to use the correct sign for each term based on the origin and direction of postive distance that you choose.

A different (and perhaps easier) approach would be to write a single equation that represents the distance between the two bikers. The time you are looking for is the time at which the distance between them is zero.