Question 6597
We'll work with the equation r * t = d. In this situation, we have two different rates and two different times but the same distance. Let's label some variables:


{{{ r[w] }}} = walking speed
{{{ r[r] }}} = running speed, which really is {{{ r[w] + 5 }}}
{{{ t[w] }}} = time it took her to run to the park, which is 1/2 hour
{{{ t[r] }}} = time it took her to walk, which is 1 1/3 hours (that's 1 hour and 20 minutes in fraction form)


Since she will walk and run the same distance, we can say


{{{ r[w]*t[w] = r[r]*t[r] }}} <---- We are actually interested in finding the distance, but in this case, we have to find the rates first.


{{{ r[w]*(4/3) = (r[w]+5)*(1/2) }}} <----- We did some substitutions and turned 1 1/3 to an improper fraction.


{{{ 4r[w] = 3(r[w]+5)(1/2) }}} <---- multiply both sides by 3 to get rid of the fraction.


{{{ 8r[w] = 3(r[w] + 5) }}} <---- multiply both sides by 2 to get rid of the other fraction


{{{ 8r[w] = 3r[w] + 15 }}} <---- expand using distributive property for the right side


{{{ r[w] = 3 }}} <----- Her walking speed was 3 miles per hour. Since it took her 1 hour and 20 minutes (4/3 of an hour) to walk at 3 miles per hour, the distance would've been r*t = (3)*(4/3) = 4 miles.