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? 
:
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/60}}} = {{{3/s}}}
Cross mult
ds = 180
:
Train time to B = Bike time to B
{{{(d+8)/60}}} = {{{5/s}}}
Cross multiply
s(d+8) = 300
ds + 8s = 300
:
Replace ds with 180
180 + 8s = 300
8s = 300 - 180
8s = 120
s = {{{120/8}}}
s = 15 mph speed of the bike
: