Question 864405
Making a table is often easiest for this, but a picture might help too.


RT=D, rate, time, distance.


Family__________rate_________time_________distance
DaVinci_________55___________t
Fermat__________65___________t
Total_____________________________________180



The question asks about time and distance or position between Portland and Seattle when the two families are at the same place.  The "when" is the time quantity, t.  Use RT=D relationship for uniform rates for motion to get an expression for distance traveled for each family.


Family__________rate_________time_________distance
DaVinci_________55___________t____________55t
Fermat__________65___________t____________65t
Total_____________________________________180


The key equation to obtain from examining this data is the sum of the distances being 180 miles.
{{{55t+65t=180}}}
{{{t=18/12=9/6=highlight(3/2)}}} hours.  This is {{{1&1/2*hours}}}.


WHERE MEET?
DaVinci family left from Seattle, going to Portland.  They will be {{{55*(3/2)=highlight(82&1/2)}}} miles from Seattle heading toward Portland when they are at the same position as the Fermat family.