If they meet in 2 hours, what is the rate of the faster car

Question

Two cars leave towns
400
kilometers apart at the same time and travel toward each other. One car's rate is
18
kilometers per hour more than the other's. If they meet in
2
hours, what is the rate of the faster car

hours, what is the rate of the faster car

Answer 1

Hi Morgan,

 

Let's begin by writing expressions to represent our unknowns:

    x = rate of slower car

    x + 18 = rate of faster car

 

Next, let's write an equation to express the sum of each car's distance traveled in 2 hours as the total distance of 400 km (distance = rate x time):

    (x)(2) + (x + 18)(2) = 400

 

Now we'll solve our equation for our unknowns:

    (x)(2) + (x + 18)(2) = 400

    2x + 2x + 36 = 400

    4x + 36 = 400

    4x = 400 - 36

    4x = 364

    x = 364/4 

    x = 91 km/hr (rate of slower car)

    x + 18 = 91 + 18

    x + 18 = 109 km/hr (rate of faster car)

 

Finally, we can check our answers by plugging them back into our original equation and see if sum of the distances for both cars equals the total distance:

    (x)(2) + (x + 18)(2) = 400

    (91)(2) + (109)(2) = 400

    182 + 218 = 400

    400 = 400 (sum = total)

 

Since the sum of the distances for both cars equals the total distance, we are confident that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.