Simple Velocity Problem: Solving for Time with Two Traveling Cars

[jk4]

Homework Statement

How long does it take an automobile traveling 60.0 km/h to become even with a car that is traveling in another lane at 40.0 km/h if the cars' front bumpers are initially 125 m apart?

Homework Equations

$$v_{average} = \frac{\Delta x}{\Delta t}$$

The Attempt at a Solution

I'll just give an explanation because it seems like a pretty simple problem. I'm just getting a different answer than the book. Here goes:
I set the distance for the 60km/h car to d+125m since it has to travel the same distance as the 40km/h car plus the extra 125m that it had to catch up. Then I solved them for the variable (d) and set the 2 equations equal to each other, and then finished solving for time.
I ended up with: 6.25 seconds The book says it takes: 22.5 seconds
the books answer seems wrong to me... can anyone verify this, or let me know what I did wrong? Thank you.

 

[lzkelley]

22.5 s is correct; I'm not sure what went wrong with your calculations.. they sound about right.
The easiest way to do this: imagine that the 40 km/h car is stationary (move to its reference frame), initially 125 m from the 60 km/h car.
What velocity is the 60 km/h car going in this new reference frame (hint: what's the difference in their velocities).
How long will it take to close the 125m distance at that speed?

 

[jk4]

I was getting the units wrong. Thanks for you help.