Question

Two cars travel at the same speed to different destinations. Car A reaches its destination in 12 minutes. Car B reaches its destination in 18 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel?

Answer 1

By setting up a system of equations and solving for the distance Car A travels, we find that the distance is 8 miles. Then, we calculate the speed to be 2/3 miles per minute, which is equivalent to 40 miles per hour.

Step-by-step explanation:

The speed of the cars can be found by using the distance-time relationship where speed is equal to distance divided by time. Since both cars travel at the same speed, we can set up a system of equations to solve for that speed.

Let's denote the speed of the cars as 's' (in miles per minute), the distance Car A travels as 'd', and therefore Car B travels 'd + 4' miles.

For Car A, we have the equation:

s = d / 12

For Car B, we have the equation:

s = (d + 4) / 18

Since the speeds are the same, we can equate these two expressions and solve for 'd':

d / 12 = (d + 4) / 18

Multiplying both sides by 36 (the least common multiple of 12 and 18) to clear the fractions, we get:

3d = 2d + 8

Subtracting 2d from both sides, we find that 'd' is equal to 8. Now, we plug this back into one of the speed equations:

s = 8 / 12

This simplifies to:

s = 2/3 miles per minute, or to convert to miles per hour (mph), we multiply by 60 (minutes in an hour):

s = 40 mph