Problema Solution
A tri-athlete dives from a bridge into a river and swims upstream through the water
for 1 hour at constant speed. She then turns around and swims downstream through the water at
the same rate of speed. As the swimmer passes under the bridge, a bystander tells her that her
hat fell into the river when she originally dived in. The swimmer continues downstream at the
same rate of speed, catching up with the hat at another bridge exactly 1 mile downstream from
the first one.
What is the speed of the current in miles per hour?
Answer provided by our tutors
let
v = the speed of the swimmer in still water, v>0
c = mph speed of the current, c>0
downstream speed: v + c
upstream speed: v - c
since speed = distance/time we have time = distance/speed and the time of the travel upstream = the time of the travel downstream
in 1 hour
she swims 1*(v - c) miles upstream
the swimmer then turns around and swims downstream the distance of (v-c) miles
the time of the swimmer downstream to the first bridge is (v - c)/(v + c) hours
and we have another 1 mile to the other bridge in time
this 1 mile the swimmer is passing in 1/(v + c) hours
the total time of the swim for the swimmer and for the hat is the same
t = 1 + (v - c)/(v + c) + 1/(v + c) hours
the distance from the the bridge to the catching up
t*c = 1
(1 + (v - c)/(v + c) + 1/(v + c))*c = 1
by solving we find c = 0.5 mph
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