Question

Doug, who runs track for his high school, was challenged to a race by his younger brother, matt. Matt started running first, and doug didn’t start running until matt had finished a quarter-mile lap on the school track. Doug passed matt as they both finished their sixth lap. If both boys ran at a constant speed, with doug running 2 miles an hour faster than matt, what was matt’s speed?.

Answer 1

By setting up an equation based on the relative distances run by Doug and Matt and solving for Matt's speed, we find that Matt's speed is 48 miles per hour.

Step-by-step explanation:

The problem is a classic relative motion problem where Doug and Matt are running with different constant speeds, and we need to find Matt's speed based on the information provided. We know that Matt ran a quarter-mile head start and that Doug runs 2 miles per hour faster than Matt. When they both finish their sixth lap, it means Doug ran 6 laps while Matt ran 5.75 laps since he had a quarter-mile head start.

Let's define Matt's speed as x miles per hour. Therefore, Doug's speed would be x + 2 miles per hour. Since distance is equal to speed multiplied by time, and we assume they ran for the same amount of time when Doug caught up to Matt, we can set up the following equation representing the distance each ran:
Doug's distance (6 laps) = Matt's distance (5.75 laps)

6(x + 2) = 5.75x

Now we solve for x:

6x + 12 = 5.75x
6x - 5.75x = -12
0.25x = -12
x = 12 / 0.25
x = 48

Therefore, Matt's speed is 48 miles per hour.