Question 713058
Enter information in this table from the problem description.  Some information is not directly given and we may need some or all of it.  We'll find out as we go.


Condition___________Rate___________Time_____________Distance
Alert_______________r______________(__)______________130
Tired_______________r-5____________(__)______________(__)
TOTAL______________________________ 3_________________190


The missing times and distance are easy enough to calculate.  Times are by distance/rate=time.  Missing distance for "tired" is by difference.


Condition___________Rate___________Time_____________Distance
Alert_______________{{{r}}}______________({{{130/r}}})____________130
Tired_______________{{{r-5}}}____________({{{60/(r-5)}}})__________(60)
TOTAL______________________________ 3_________________190



The most sensible way to continue from the completed table is use the sum of the times.
 
{{{highlight(130/r+60/(r-5)=3)}}}, solve for r. (Lowest Common Denominator to start solving the equation is {{{r*(r-5)}}}.)