Question 947415
{{{x}}}= Judy's speed in miles per hour.
"He (Roger) went three times as fast as her (Judy)" translates as
{{{3x}}}= Roger's speed in miles per hour.
We calculate travel time as distance divided by speed, so
{{{375/x}}}= travel time for Judy, in hours.
{{{375/3x}}}= travel time for Roger, in hours.
"Roger made the 375 mile trip in 10 hours less than it took Judy" translates as
{{{375/3x=375/x-10}}}
and that is our equation.
Solving:
{{{375/3x=375/x-10}}}
There are many ways to solve it. I will show the two I thought of first.
 
One way:
Multiplying both sides of the equal sign times {{{3x}}} we get
{{{3x(375/3x)=3x(375/x-10)}}}
{{{375=3(375)-30x)}}}
{{{375=1125-30x}}}
{{{375-1125=-30x}}}
{{{-750=-30x}}}
{{{(-750)/(-30)=x}}}
{{{highlight(x=25)}}} and {{{3x=3*25=highlight(75)}}}
 
Another way:
{{{375/3x=375/x-10}}}--->{{{375/x-375/3x=10}}} (which is the first equation I wrote)
Using {{{3x}}} as a common denominator
{{{(375*3-375)/3x=10}}}
{{{375(3-1)/3x=10}}}
{{{375*2/3x=10}}}
{{{750/3x=10}}}
Then, I simplify, dividing both sides by {{{10}}} to get
{{{75/3x=1}}}
and multiplying both sides times {{{x}}} , I get
{{{75/3=x}}}
{{{highlight(x=25)}}} and {{{3x=3*25=highlight(75)}}}


Any way you solve it, Judy was driving at {{{highlight(25)}}} miles per hour,
while Roger was driving at {{{highlight(75)}}} miles per hour.