Question

Felipe jogs for 3 miles and then walks another 3 miles. He jogs 1 and 1/2 miles per hour faster than he walks, and the entire distance of 6 miles takes 3 hours. Find the rate at which he walks and the rate at which he jogs.

Answer 1

Answer:

• walking: 1.5 mph
• jogging: 3 mph

Step-by-step explanation:

Let w represent Felipe's walking speed in miles per hour. Then his total travel time is ...

  time = distance/speed

  3 = 3/w +3/(w+1.5) . . . . . total time is the sum of walking and jogging times

  1 = 1/w +1/(w +1.5) . . . . . divide by 3

  w(w +1.5) = (w+1.5) +w . . . . multiply by w(w+1.5)

  w^2 -0.5w -1.5 = 0 . . . . . . subtract 2w+1.5

  (w -1.5)(w +1) = 0 . . . . . . . factor

The values of w that make this equation true are w = 1.5 and w = -1. Only the value 1.5 makes any sense in this scenario. Felipe's jogging speed is then 1.5+1.5 = 3 mph.

Felipe walks at 1.5 mph and jogs at 3 mph.