Word Problem

Question

One person runs 3 miles per hour faster than a second person. The first person runs 3 miles in the same time the second person runs 2 miles. Find the speed of each person.

Answer 1

Distance = Rate * Time, or D = R*T 

 

Let R = Rate of 2nd person

Then R + 3 = Rate of 1st person 

 

Let T = Time (same for each) 

 

3 = (R+3)*T = R*T + 3*T  for 1st person

2 = R*T                            for 2nd person

 

Subtract the 2nd equation from the 1st 

 

1 = 3*T

T = (1/3) hour 

 

For the 2nd person R = 2/T = 2/(1/3) = 2*(3/1) = 6 mph 

So for the 1st person R = 9 mph  

 

Check:  D = 9 mph * (1/3) hour = 3 miles for 1st person

            D = 6 mph * (1/3) hour = 2 miles for 2nd person