Katie walked from her home to the fitness center at 6km/h. She stayed 45 minutes and then got a ride back home at 48km/h.

Question

If she returned 1.5 hours after starting out, find the distance of her house to gym?

Answer 1

Let x be the distance. Then

time going to gym + time returning from gym = 1.5 -0.75 (0.75 hrs is how long she was at the gym)

x/6 +x/48 = 0.75 (1.5-0.75=0.75 and using the formula time=distance/velocity )

48(x/6 + x/48) = 0.75 × 48 (multiplying both sides by 48 to get rid of the fraction)

8x + x = 36

9x = 36

x = 4 km

Answer 2

Let x = time it takes to go to the fitness center.  Then the time it takes to return home = 1.5 - 0.75 - x = 0.75 - x.  (45 minutes = 0.75 hours)

 

Distance = (rate)(time)

 

Distance to fitness center = distance from fitness center

 

So, 6x = 48(0.75 - x)

     6x = 36 - 48x

     54x = 36

        x = 36/54 = 2/3 hours

 

Therefore, distance from the house to the gym = 6x = 6(2/3) = 4 km.