SOLUTION: Mike was racing in a bike marathon. He was 3/8 of the way across a narrow bridge when he heard the Wabash Cannonball train approaching the bridge from behind him at 60 miles per ho

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Question 191930: Mike was racing in a bike marathon. He was 3/8 of the way across a narrow bridge when he heard the Wabash Cannonball train approaching the bridge from behind him at 60 miles per hour. Being an amateur mathematician as well as a marathon biker, Mike calculated that he could just reach either end of the bridge at the same time as the train. How fast was Mike pedaling his bike?
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Mike was racing in a bike marathon. He was 3/8 of the way across a narrow bridge
when he heard the Wabash Cannonball train approaching the bridge from behind
him at 60 miles per hour. Being an amateur mathematician as well as a marathon
biker, Mike calculated that he could just reach either end of the bridge at the
same time as the train. How fast was Mike pedaling his bike?
:
Let s = speed of the bike
:
Let the bridge length = 8 units (A to B)
bike (X) is 3 units from the left side and 5 units from the right side
:
Let train dist from bridge = d
:
Train-------d---------A=========X===================B-----------
:
Time equation
Train time to A = Bike time to A
d%2F60 = 3%2Fs
Cross mult
ds = 180
:
Train time to B = Bike time to B
%28d%2B8%29%2F60 = 5%2Fs
Cross multiply
s(d+8) = 300
ds + 8s = 300
:
Replace ds with 180
180 + 8s = 300
8s = 300 - 180
8s = 120
s = 120%2F8
s = 15 mph speed of the bike
: