A long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles...
A long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?
Do not do any rounding.
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
The long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles per hour.
Let the cyclist overtake the runner after T hours.
The distance traveled by the runner when the cyclist overtakes him is 5*(T + 3) and the distance traveled by the cyclist is T*8
Equating the two, 5T + 15 = 8T
=> 3T = 15
=> T = 5
The cyclist overtakes the runner after traveling for 3 hours.