Question 124676
Let {{{t[1]}}}=walking time and {{{t[2]}}}=driving time



Now we're going to use the distance-rate-time equation {{{d=rt}}}


Since the walking speed is 4 mph and the walking time is {{{t[1]}}}, this means {{{r=4}}} and {{{t=t[1]}}} 


{{{d=4t[1]}}} Plug in {{{r=4}}} and {{{t=t[1]}}}




Also, since the driving speed is 20 mph and the driving time is {{{t[2]}}}, this means {{{r=20}}} and {{{t=t[2]}}} 


{{{d=20t[2]}}} Plug in {{{r=20}}} and {{{t=t[2]}}}



Because the distance is the same both ways, this means that {{{d=4t[1]=20t[2]}}} 



 {{{4t[1]=20t[2]}}} Start with the given equation



 {{{t[1]=5t[2]}}} Divide both sides by 4 to isolate {{{t[1]}}}





If the entire trip took 1 hour and 40 minutes and there was a 10 minute wait, then the traveling portion took 1 hour and 30 minutes (which is 1.5 hours)



So the sum of these two times is 1.5. In other words, we have this first equation



{{{t[1]+t[2]=1.5}}}



{{{5t[2]+t[2]=1.5}}} Plug in {{{t[1]=5t[2]}}} 



{{{6t[2]=1.5}}} Combine like terms



{{{t[2]=0.25}}} Divide both sides by 6 to isolate {{{t[2]}}}



So the driving time is 0.25 hours or 15 minutes


Now let's go back to the equation {{{d=20t[2]}}} 



{{{d=20t[2]}}} Start with the given equation



{{{d=20(0.25)}}} Plug in our answer {{{t[2]=0.25}}}



{{{d=5}}} Multiply



So the distance that she traveled is 5 miles