Question 989052

Jeff leaves home and rides his bicycle out into the country for 3 hours.  On his return trip along the same route, it takes him three-quarters of an hour longer.  If his rate on the return trip was 2 miles per hour slower than on the trip out into the country, find the total roundtrip distance.
<pre>Let one-way distance be D
Then outbound speed = {{{D/3}}}, and return-trip speed = {{{D/3 - 2}}}
Since return trip took ¾ hour longer, then return trip took {{{3 + 3/4}}}, or {{{15/4}}} hours
Thus, it can be said that: {{{D = (15/4)(D/3 - 2)}}}
{{{D = 15D/12 - 15/2}}}
12D = 15D - 90 -------- Multiplying by LCD, 12 
12D - 15D = - 90 
- 3D = - 90
D, or one-way distance = {{{(- 90)/(- 3)}}}, or 30 miles
Round-trip distance: 2(30), or {{{highlight_green(60)}}} miles