SOLUTION: the smiths are moving across the country mr smith leaves 3 hours before mrs smith. if he averages 65 and she averages 90 mph how long will it take mrs smith to overtake mr smith

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Question 716813: the smiths are moving across the country mr smith leaves 3 hours before mrs smith. if he averages 65 and she averages 90 mph how long will it take mrs smith to overtake mr smith
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
He has a head start of
+d%5B1%5D+=+65%2A+3+
+d%5B1%5D+=+195+ mi
start a stopwatch when the wife leaves
Let +t+ = time on stopwatch when they meet
Let +d+ = distance the wife has to travel
until she overtakes him
His equation:
(1) +d+-+195+=+65t+
Her equation:
(2) +d+=+90t+
--------------
Substitute (2) into (1)
(1) +90t+-+195+=+65t+
(1) +25t+=+195+
(1) +t+=+7.8+
+.8+ hrs = +.8%2A60+=+48+ min
She will overtake him in 7 hrs 48 min
check:
(2) +d+=+90%2A7.8+
(2) +d+=+702+ mi
and
(1) +d+-+195+=+65%2A7.8+
(1) +d+=+507+%2B+195+
(1) +d+=+702+ mi
OK