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Two cars leave towns 800 kilometers apart at the same time and travel toward each other. One car's rate is 14 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car?

Answer :

The rate of the slower car is 93 kilometers per hour.

Two cars leave towns that are 800 kilometers apart and travel towards each other. Let's call the rate of the faster car "r" kilometers per hour. Since the other car's rate is 14 kilometers per hour less than the faster car, its rate is "r - 14" kilometers per hour.

When they meet after 4 hours, they would have traveled a combined distance of 4 hours multiplied by the sum of their rates.

Distance = Rate × Time

For the faster car:

Distance = r × 4

For the slower car:

Distance = (r - 14) × 4

Since they meet in the middle (800 kilometers apart), the sum of their distances will be equal to 800 kilometers:

r × 4 + (r - 14) × 4 = 800

Simplify the equation:

4r + 4r - 56 = 800

Combine the terms:

8r - 56 = 800

Add 56 to both sides:

8r = 856

Now, solve for "r" by dividing both sides by 8:

r = 856 / 8

r = 107

So, the rate of the faster car is 107 kilometers per hour. To find the rate of the slower car, subtract 14 from the faster car's rate:

Slower car's rate = 107 - 14 = 93 kilometers per hour.

Therefore, the rate of the slower car is 93 kilometers per hour.

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