Joan and her brother Justin left a hotel at the same time, driving in opposite directions at constant rates. After traveling for 4 hours, they were 480 miles apart. If Justin drove 10 miles per hour faster than Joan, how fast did Joan drive?
To find out how fast Joan drove, we need to set up an equation based on the given information.
Let's assume that Joan's speed is represented by x miles per hour. Since Justin drives 10 miles per hour faster than Joan, his speed will be (x + 10) miles per hour.
Distance = Speed * Time
Distance that Joan travels in 4 hours = 4 * x = 4x miles
Distance that Justin travels in 4 hours = 4 * (x + 10) = 4x + 40 miles
According to the information given, Joan and Justin were 480 miles apart after traveling for 4 hours. This means that the sum of the distances they traveled individually is equal to 480 miles.
4x + 4x + 40 = 480
Combining like terms:
8x + 40 = 480
Now, we can solve for x:
8x = 480 - 40
8x = 440
x = 440 / 8
x = 55
Therefore, Joan drove at a speed of 55 miles per hour.
Let x = Joan's speed
4x + 4(x+10) = 480
Solve for x.