SOLUTION: ryan left the science museum and drove south. Gabriella left three hours later driving 42km/h faster in an effort to catch up to him. 2 hours later, Gabriella finally caught up. Fi

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: ryan left the science museum and drove south. Gabriella left three hours later driving 42km/h faster in an effort to catch up to him. 2 hours later, Gabriella finally caught up. Fi      Log On

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Question 920808: ryan left the science museum and drove south. Gabriella left three hours later driving 42km/h faster in an effort to catch up to him. 2 hours later, Gabriella finally caught up. Find Ryan's average speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Ryan's average speed
What is Ryan's head start in km?
+d%5B1%5D+=+s%2A3+
-----------------
Start a stopwatch when Gabriella leaves
Stop the stopwatch 2 hrs later when
she catches up with Ryan
Let +d+ = the distance in km that
Gabriella travels until she catches him
-----------------
Ryan's equation:
(1) +d+-+3s+=+s%2A2+
Gabriella's equation:
(2) +d+=+%28+s+%2B+42+%29%2A2+
----------------------
(1) +d+=+2s+%2B+3s+
(1) +d+=+5s+
Substitute (1) into (2)
(2) +5s+=+2s+%2B+84+
(2) +3s+=+84+
(2) +s+=+28++
Ryan's average speed is 28 km/hr
check:
+s+%2B+42+=+28+%2B+42+
+s+%2B+42+=+70+
-----------------
(1) +d+=+5%2A28+
(1) +d+=+140+
and
(2) +d+=+%28+s+%2B+42+%29%2A2+
(2) +d+=+70%2A2+
(2) +d+=+140+
OK