SOLUTION: ariel wolfman and bryce dettloff each average 30 km/h for the first hour of a 100 km race. at the end of the hour bryce has a mishap, and loses 12 minutes. ariel finishes the remai

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Question 495045: ariel wolfman and bryce dettloff each average 30 km/h for the first hour of a 100 km race. at the end of the hour bryce has a mishap, and loses 12 minutes. ariel finishes the remainder of the race at an average rate of 25 km/h. if bryce averages 27.5 km/h after resuming, will he catch ariel before the finish line?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For 1 hour the distance is:
+30%2A1+=+30+ km
There is +100+-+30+=+70+ km left
Ariel gets ahead by
+25%2A%2812%2F60%29+=+5+ km
So Ariel only has to go +70+-+5+=+65+ km
to the finish
Assume d is the distance that Ariel will go
when Bryce catches him
For Bryce:
(1) +d+%2B+5+=+27.5%2At+
For Ariel:
(2) +d+=+25%2At+
---------------
(2) +t+=+d%2F25+
(1) +d+%2B+5+=+27.5%2A%28d%2F25%29+
(1) +25d+%2B+125+=+27.5d+
(1) +2.5d+=+125+
(1) +d+=+50+
Bryce will catch Ariel before the finish line,
since Ariel has 65 km to go when Bryce resumes
after mishap