Worded Equation problems

Question

Phoebe Spends 2 hours training for a race. She runs full speed at 8 Miles per hour for the race distance, then she walks back to the starting point at 2 miles per hour. How long does she spend walking? How long does she spend running?

Answer 1

d=rt

d=8t

d=2(2-t)

8t=2(2-t)

4t=2-t

4t+t=2

5t=2

t=2/5 of an hour or 24 minutes running

2- 2/5=1 3/5 hours or 1 hour 36 minutes walking

Answer 2

 

Rate • Time = Distance

 

Let t_r = time she ran

Let t_w = time she walked

 

RUNNING THE RACE:

  

    Rate • Time = Distance

    8 t_r = Distance

 

WALKING THE RACE:

 

    Rate • Time = Distance

    2 t_w = Distance 

 

--------------------------------

 

The distance for each leg is the same (ran the distance, walked the return distance)

 

     8t_r = 2t_{w     (Equation 1)}

 

The total time was 2 hours

 

     t_r + t_w = 2    (Equation 2)

 

Solving Equation 2 for t_r,  t_r = 2 - t_w

 

Substituting 2-t for t_r in equation 1, then solving for t_w

 

    8(2 - t_w) = 2t_w 

    16 - 8t_w = 2t_w

    16 = 2t_w + 8t_w

    16 = 10t_w

    10t_w = 16

    t_w = 16/10

    t_w = 1.6

 

She walked for 1.6 hours ... 1 hour, 36 minutes

She ran for 2 - 1.6 hours = .4 hours = 24 minutes