SOLUTION: the penguin was 1200 yards ahead when batman began his pursuit. if batman ran 3 times as fast as the penguin and overtook him in 30 minutes, how fast did each one run

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Question 533119: the penguin was 1200 yards ahead when batman began his pursuit. if batman ran 3 times as fast as the penguin and overtook him in 30 minutes, how fast did each one run
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the penguin's speed in feet/min
Let +d+ = distance covered by Batman until he catches Penguin
Batman's speed = +3p+
-----------------------
given:
Penguin's head start was +3%2A1200+=+3600+ ft
Start a stopwatch when Batman leaves. Now they both run
for the same amount of time
Batman:
(1) +d+=+3p%2A30+
Penguin:
(2) +d+-+3600+=+p%2A30+
Substitute (1) into (2)
(2) +90p+-+3600+=+30p+
(2) +60p+=+3600+
(2) +p+=+60+
and
++3p+=+180+
Penguin ran 60 ft/min
Batman ran 180 ft/min
check:
(1) +d+=+3p%2A30+
(1) +d+=+3%2A60%2A30+
(1) +d+=+5400+
and
(2) +d+-+3600+=+p%2A30+
(2) +5400+-+3600+=+p%2A30+
(2) +1800+=+30p+
(2) +p+=+60+
OK