What is the distance of the race?

Question

Phil has one hour to spend training for the race. He runs the full distance of the race at 8 miles per hour and walks back at 2 miles per hour. What is the distance of the race?

Answer 1

Let D = the race distance (in miles), and let T = time spent running (in hours)  

 

Phil ran at 8 mph  ==>  D = 8*T  

 

If he had 1 hour total and spent T hours running then he spent (1 - T) hours walking (the same distance)  

 

He walked at 2 mph  ==>  D = 2*(1 - T)  

 

Substitute the value for D from the 1st equation into the 2nd equation to get  

 

8*T = 2*(1 - T)

8*T = 2 - 2*T

10*T = 2

T = 0.2  hours  

 

Plug this value for T into the 1st equation to get  D = 8*0.2 = 1.6 miles  

 

Check:  Run distance = (8 mph)*(0.2 hours) = 1.6 miles

           Walk distance = (2 mph)*(0.8 hours) = 1.6 miles

           Total time = 0.2 + 0.8 = 1 hour  

Answer 2

Distance = Rate x Time

 

in this case, T = 1 hour

 

Rate = average of the two rates given; (8mph + 2mph)/2 = 5mph

 

Distance = 5miles/hour x 1 hour

 

Distance = 5 miles