Question

Suppose that during a test drive of two​ cars, one car travels 234 miles in the same time that a second car travels 180 miles. If the speed of the first car is 12 miles per hour faster than the speed of the second​ car, find the speed of both cars.

Answer 1

Let x = speed of first car x + 12 = speed of second

Explanation:

Answer 2

Let's denote the speed of the second car as x (in miles per hour). Then the speed of the first car is 12 miles per hour faster, which is x + 12.

We know that both cars traveled the same amount of time, so we can use the formula:

distance = speed × time

For the first car, we have:

234 = (x + 12) × time

For the second car, we have:

180 = x × time

We want to find the speeds of both cars, so we need to solve for x and x + 12. We can start by solving for time in both equations:

time = 234 / (x + 12)

time = 180 / x

Since both expressions are equal to time, we can set them equal to each other:

234 / (x + 12) = 180 / x

To solve for x, we can cross-multiply and simplify:

234x = 180(x + 12)

234x = 180x + 2160

54x = 2160

x = 40

Therefore, the speed of the second car is 40 miles per hour, and the speed of the first car is x + 12 = 52 miles per hour.

Explanation: