Question 1026741
A motorist travelled to a distant city in 2 hours and returned by another route that is 30 miles longer. On the return trip she travelled 10 miles per hour faster and took 6 minutes longer. Find the length of the shorter route.
<pre>Let length of shorter route be D
Then length of longer route = D + 30
Outgoing time: 2 hours, and return time = {{{2 + 6/60}}} -----> {{{2&1/10}}} -----> {{{21/10}}} hrs 
We then get the following SPEED equation: {{{D/2 = (D + 30)/(21/10) - 10}}}
{{{D/2 = (D + 30) * (10/21) - 10}}}
{{{D/2 = 10(D + 30)/21 - 10}}}
{{{D/2 = (10D + 300)/21 - 10}}}
21D = 2(10D + 300) - 420 -------- Multiplying by LCD, 42
21D = 20D + 600 – 420
21D – 20D = 180
D, or length of shorter route = {{{highlight_green(matrix(1,2, 180, "miles"))}}}