Problema Solution
The distance between two piers on a river is 43.2 miles. It takes a motorboat, moving downriver, 2 hr 24 min to complete the journey. How much time does it take the same boat to go back upstream if the current flows at 1.8 mph?
Answer provided by our tutors
v = the rate of the boat in still water
c = 1.8 mph the rate of the current
d = 43.2 mi
t1 = 2 hr 24 min = 2 + 24/60 = 2.4 hr
t2 = the of the travel back (upstream)
The rate of the boat moving downriver is: v + c
The rate of the boat moving upstream is: v - c
d/t1 = v + c
43.2/2.4 = v + 1.8
v + 1.8 = 43.2/2.4
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click here to see the equation solved for v
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v = 16.2 mph
Since speed = distance/time follows time = distance/speed:
t2 = d/(v - c)
t2 = 43.2/(16.2 - 1.8)
t2 = 3 hr
The boat needs 3 hours to go back upstream.