Dustin drives 5 miles per hour faster than Kelly. If he leaves town 1 hour after Kelly and they travel in opposite directions, they will have drive equal distances after Dustin has traveled 7 hours. How far apart are they?
To find out how far apart they are, we need to calculate the distance traveled by each person. Let's break down the information given:
1. Dustin drives 5 miles per hour faster than Kelly.
2. Dustin leaves town 1 hour after Kelly.
3. They travel in opposite directions.
4. After Dustin has traveled 7 hours, they will have driven equal distances.
First, let's determine Kelly's speed. Since Dustin drives 5 miles per hour faster, we'll consider Kelly's speed as "x" miles per hour. Therefore, Dustin drives at a speed of "x + 5" miles per hour.
Now, let's calculate the distance traveled by Kelly in 7 hours. Since distance is equal to speed multiplied by time, Kelly's distance is given by:
Kelly's distance = Kelly's speed × Kelly's time
= x miles/hour × 7 hours
= 7x miles
Next, let's calculate Dustin's distance. Since he leaves town 1 hour after Kelly, his time travel is reduced by 1 hour (i.e., 7 - 1 = 6 hours). Therefore, Dustin's distance is given by:
Dustin's distance = Dustin's speed × Dustin's time
= (x + 5) miles/hour × 6 hours
= 6(x + 5) miles
According to the problem, Kelly's and Dustin's distances are equal after 7 hours. Therefore, we can set up the following equation:
Kelly's distance = Dustin's distance
7x = 6(x + 5)
Now let's solve the equation:
7x = 6x + 30
7x - 6x = 30
x = 30
So, Kelly's speed is x = 30 miles per hour.
To find the distance between Kelly and Dustin, we can substitute this value back into one of the distance formulas:
Kelly's distance = 7 × 30
= 210 miles
Thus, they are 210 miles apart.