Solving a distance, rate, time problem using a linear equation.

Question

A long distance runner starts at the beginning of a trail and runs at a pace of 4 miles per hour. One hour later, a cyclist starts at the beginning of the trail and travels at a rate of 20 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

Answer 1

the runner goes 4 mile per hour so after one mile he will be 4 mile ahead and that is when cyclist start so when the distance of cyclist will be the same as distance of runner? the answer to this question is will be the time that he will over take. This time we call it  "t"

 

so

 

4+4t   will be the distance of runner after time t

 

20t      will be the distance of cyclist after time t

 

so

 

20t=4+4t

 

so subtract 4t from both sides

 

16t=4 divide both sides by 16

 

t=1/4 of an hour or you can say 15 min