Erika drive from Ottawa at 80km/h. Julie left Ottawa 1h later and drove along the same road at 100km/h. How far from Ottawa did Julie overtake Erika

Question

Solve using substitution, elimination or graphing. 

Answer 1

Let us assume that the distance from Ottawa at which they meet each other is 'x' km. Then the time it took For Erika to travel this distance is:

 

t_Erika = x/80

 

Julie started 1 hour after Erika. So the time it took for Julie to cover that 'x' distance is (including the 1 hour delay time):

 

t_Julie = 1 + x/100

 

These two times must be equal to each other since they meet at this point of time. Setting them equal and solving for x:

 

t_Erika = t_Julie

x/80 = 1 + x/100

x/80 - x/100 = 1

5x/400 - 4x/400 = 1

(5x-4x)/400 = 1

x/400 = 1

x = 400 km