Math CentralQuandaries & Queries


Question from Jennifer, a student:

two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea?

Hi Jennifer.

First step: you need to identify what are the unknown quantities the question asks for and assign them a variable name.

What is the speed of each car?
So let x = the speed of the slower car and y = the speed of the faster car.

Are they related to each other? Yes: the faster car is travelling 15 mph faster. This gives us the first equation!

x + 15 = y

For a "system of equations" we are looking for as many equations as there are unknowns. Since we are trying to discover two quantities (x and y), we need two equations, so we need to dig in the question for another relevant relationship.

So take a look at the different kinds of quantities involved: time, distance, speed. What relationship do these have?
Time * Speed = Distance !

So now comes the hard part: We must write an equation that combines the speed and distance of each car, adding them together to get the total distance....

3.5x + 3.5y = 420

This gives us our two equations! That's the hard part done.

Now you can use either the elimination method or the substitution method (substitution method is easier for this question) to solve this system. If you want to see examples of these, then look up "elimination method" or "substitution method" in our Quick Search.

Hope this helps,
Stephen La Rocque

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