SOLUTION: Justin starts at a point 26 miles from home and runs toward home at 6 mph. Rhonda starts from home 1.3 hours later and pedals toward Justin at 8 mph. How long has Justin been runni

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Justin starts at a point 26 miles from home and runs toward home at 6 mph. Rhonda starts from home 1.3 hours later and pedals toward Justin at 8 mph. How long has Justin been runni      Log On


   

Question 673552: Justin starts at a point 26 miles from home and runs toward home at 6 mph. Rhonda starts from home 1.3 hours later and pedals toward Justin at 8 mph. How long has Justin been running when he meets Rhonda? How far from home do they meet?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Justin gets a head start of
+6%2A1.3+=+7.8+ mi
They are then +26+-+7.8+=+18.2+ mi apart
----------------
Let +d+ = the distance Rhonda now has
to cover to meet Justin.
+18.2+-+d+ = distance Justin now has to cover
Let +t+ = the time it now takes them to meet
------------
After Justin's head start:
Justin's equation:
(1) +18.2+-+d+=+6t+
Rhonda's equation:
(2) +d+=+8t+
-------------
Substitute (2) into (1)
(1) +18.2+-+8t+=+6t+
(1) +14t+=+18.2+
(1) +t+=+1.3+ hrs
and
(1) +18.2+-+d+=+6%2A1.3+
(1) +18.2+-+d+=+7.8+
(1) +d+=+18.2+-+7.8+
(1) +d+=+10.4+
Justin has been running for +1.3+%2B+1.3+=+2.6+ hrs
Rhonda travels +d+=+10.4+ mi from home
where they meet