Question 395892
It took Emily 25 minutes to ride her bicycle to the repair shop and 1 hour and
 15 minutes to walk back home.
 If Emily can ride her bicycle 8km/h faster than she can walk, how far is the
 repair shop from her house?"
:
Change 25 min: 25/60 = {{{5/12}}} hrs
Change 1 hr 15 min to: {{{5/4}}} hrs
:
First find out how fast she can walk
let s = walking speed
then
(s+8) = biking speed
:
The distance riding and distance walking are the same, write a dist equation:
dist = speed * time
:
{{{5/12}}}(s+8) = {{{5/4}}}s
Multiply both sides by 12 to get rid of the denominators
5(s+8) = 3(5s)
5s + 40 = 15s
40 = 15s - 5s
40 = 10s
s = 4 mph is her walking speed
then
4 + 8 = 12 mph is her biking speed
:
Find the distance
{{{5/4}}} * 4 = 5 mi is the distance to the repair shop
:

Check the distance
{{{5/12}}} * 12 = 5 mi; confirms our solution