Kyle and his brother Joel leave a rest stop at the same time traveling in opposite directions. After traveling for 6 hours, they are 780 miles apart. If Kyle drives 10 miles per hour faster than Joel, how fast was Joel traveling?
60 mph
Let's assume that Joel's speed is J miles per hour. According to the given information, Kyle drives 10 miles per hour faster than Joel, so Kyle's speed can be calculated as J + 10 miles per hour.
To find the solution, we will use the formula: Distance = Speed × Time.
Given that Kyle and Joel travel in opposite directions, we can add their distances. Joel travels for 6 hours, so his distance can be calculated as J × 6 miles. Similarly, Kyle's distance can be calculated as (J + 10) × 6 miles.
Adding the distances together, we have:
(J × 6) + ((J + 10) × 6) = 780 miles.
Simplifying this equation, we get:
6J + 6(J + 10) = 780.
Expanding the equation, we have:
6J + 6J + 60 = 780.
Combining like terms, we get:
12J + 60 = 780.
Subtracting 60 from both sides of the equation, we have:
12J = 720.
Dividing both sides by 12, we find:
J = 60.
Therefore, Joel was traveling at a speed of 60 miles per hour.
To determine Joel's speed, we need to break down the information provided and use the equation for distance, speed, and time.
Let's consider the following:
Let Joel's speed be x miles per hour.
Since Kyle drives 10 mph faster than Joel, Kyle's speed is x + 10 miles per hour.
Now, let's find the distance each person travels in 6 hours:
Joel's distance = Joel's speed × time = x miles per hour × 6 hours = 6x miles
Kyle's distance = Kyle's speed × time = (x + 10) miles per hour × 6 hours = 6x + 60 miles
Given that Kyle and Joel leave a rest stop at the same time traveling in opposite directions and are 780 miles apart after 6 hours, we can set up the following equation:
Joel's distance + Kyle's distance = Total distance apart
6x + (6x + 60) = 780 miles
Simplifying the equation:
12x + 60 = 780
12x = 720
x = 60
Therefore, Joel's speed is 60 miles per hour.