How far does Marie live from the bike shop?

[Hank T]

Marie rode her bike from her home to the bike shop and then walked back. If she averaged 5 miles per hour riding a bike and 3 miles per hour walking, how far does she live from the bike shop if her total travel time is 2 hours?

 

[Elmyr]

d = r * t
d = 5 miles/hour * t
d = 3 miles/hour * (2 - t)

5 * t = 3 * (2 - t)
5t = 6 - 3t
8t = 6
t = 6/8 = 3/4 hours

d = 5 miles/hour * 3/4 hours
d = 15/4 miles = 3 3/4 miles = 3.75 miles

Check:
5 * 3/4 + 3 * (2 - 3/4) = 15/4 * 2
15/4 + 6 - 9/4 = 30/4
15/4 + 24/4 - 9/4 = 30/4
30/4 = 30/4

 

[Krunknuttz]

approx. - 4 miles
exactly - 3.75 miles

Going 5 mph on bike 3.75 miles to the bike shop took .75 hours.
Going 3 mph walking home 3.75 miles from the bike shop took 1.25 hours.
This totals a time of 2 hours there and back.