Algebra Word Problem Help?
Two cars leave towns 212 miles apart, traveling toward each other. One car is traveling 10 miles per hour faster than the other. They pass each other 2 hours later. What are their speeds?
Note: please don't solve it for me... what i need to know is JUST the equation... i can solve it from there :) thanks!
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Okay so let's say the speeds are x and y. In that case we have the following system of equations:
x=y+10
2x+2y=212
That is the system of equations you need to solve algebraically. If you think you can do that on your own, go ahead. If you want more help, look farther down.
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If we change the first equation to get y onto the left-hand side, we have:
x-y=10
Now we can solve by the matrix method. Start by dividing the second equation by 2 to get:
x+y=106
Then add the earlier equation to this one to get:
2x=116
Divide that by 2:
x=58
Rearrange the very first equation to get:
y=x-10
Substitute the value of x to get y:
y=58-10=48
So the answer is that one car is going 58 miles per hour and the other is going 48 miles per hour.