Question 982361
Uniform Rates for Travel, RT=D relates rate, time, distance.


Let r be the unknown rate for the first part;
let d be the unknown distance of the second part;


___________________rate_____________time_____________distance
part1_______________r_______________(___)_____________60
part2______________r+15_____________(___)_____________d
TOTALS_______________________________2________________100


Form expressions for the missing time quantities from the basic idea {{{RT=D}}},
{{{RT/R=D/R}}}
{{{highlight_green(T=D/R)}}}



___________________rate_____________time_____________distance
part1_______________r_______________60/r______________60
part2______________r+15_____________d/(r+15)___________d
TOTALS_______________________________2________________100


Note that the distance sum arrangement will give the unknown part2 distance.
60+d=100
d=100-60
d=40
and you can adjust the tabulated information:


___________________rate_____________time_____________distance
part1_______________r_______________60/r______________60
part2______________r+15_____________40/(r+15)__________40
TOTALS_______________________________2________________100


The total time will give an equation in the single variable, r.
{{{60/r+40/(r+15)=2}}}
This can be partly simplified to
{{{(60/r+40/(r+15))(1/2)=2(1/2)}}}
{{{highlight_green(30/r+20/(r+15)=1)}}}


Can you solve this equation for r ?



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The algebra steps give a factorable quadratic equation, making the final answer apparent.
{{{highlight(highlight(r=45))}}}