Question 1048246
paul traveled to lexington at 70 mph. on the way back he averages 55 mph. the way back was 86 miles longer and took 2.6 hours longer to drive. how long was the scenic route from Lexington?
how long means? hours or distance? i will solve for both.

To lexington

speed 70
distance d
time     t

back

speed 55
distance d +86
time= t+2.6h

{{{70t}}}={{{55*(t+2.6)}}}
*[invoke explain_simplification "15t=143" ]
t is {{{9.5333}}}
going back time is {{{12.1333}}}
the required
d={{{v*(12.1333)}}}
d={{{55*(12.1333)}}}
d=(55)(12.1333)
d={{{(667.333)}}}
d={{{753.333}}} is the required scenic distance from lexington..

check that
70*9.5333 is {{{667.3}}}