<PRE><B>Question 153960</B>
Ryan drives to Pittsburgh at 55 mph and returns by a road 10 miles shorter at 60 mph. The return trip takes 30 minutes less. How long is each road?
:
let d = distance of the original trip
then
(d-10) = distance of the return trip
:
Convert 30 min to hrs; .5 hrs
:
Write a time equation:
:
to time = return time + one-half hr
{{{d/55}}} = {{{((d-10))/60}}} + .5
:
Multiply equation by 3300 to get rid of the denominator (55*60)
60d = 55(d-10) + 3300(.5)
:
60d = 55d - 550 + 1650
:
60d - 55d = 1100
d = {{{1100/5}}}
d = 220 mile is the original trip and 210 miles is the return trip
:
:
Check solution by finding the time for each trip
220/55 = 4 hrs
210/60 = 3.5 hrs</PRE>