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

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Question 797543: Ryan left the science museum and drove
south. Gabriella left three hours later
driving 42 km/h faster in an effort to catch
up to him. After two hours Gabriella finally
caught up. Find Ryan's average speed. Please show step by step
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Ryan's average speed in km/hr
+s%2A3+ = Ryan's head start in km
+s+%2B+42+ = Gabriella's average speed in km/hr
Let +d+ = the distance in km Gabriella travels in 2 hrs
----------------
Start a stop watch when Gabriella leaves and stop it in 2 hrs
Ryan's equation:
(1) +d+-+s%2A3+=+s%2A2+
Gabriella's equation:
(2) +d+=+%28+s+%2B+42+%29%2A2+
---------------------
substitute (2) into (1)
(1) +%28+s+%2B+42+%29%2A2+-+3s+=+s%2A2+
(1) +2s+%2B+84+-+3s+=+2s+
(1) +-s+%2B+84+=+2s+
(1) +3s+=+84+
(1) +s+=+28+
Ryan's average speed is 28 km/hr
check:
(1) +d+-+3s+=+s%2A2+
(1) +d+-+3%2A28+=+28%2A2+
(1) +d+-+84+=+56+
(1) +d+=+140+
and
(2) +d+=+%28+s+%2B+42+%29%2A2+
(2) +d+=+%28+28+%2B+42+%29%2A2+
(2) +d+=+70%2A2+
(2) +d+=+140+
OK