Problema Solution
a boat travelling upstream goes 42 miles in 7 hours. if the return trip takes only 3 hours, what is the speed ( in miles per hour ) of the boat in still water?
Answer provided by our tutors
let
d = 42 mi the distance of the travel in one direction
t1 = 7 hr the time of the travel upstream (against the current)
t2 = 3 hr the time of the travel with the current (the return trip)
c = the speed of the current, c>0
v = the speed of the boat in still water, v>0
since speed = distance/time follows speed*time = distance
traveling upstream the speed of the boat is: v - c
(v - c)t1 = d
(v - c)7 = 42 divide both sides by 7
v - c = 6
traveling downstream the speed of the boat is: v + c
(v + c)t2 = d
(v + c)3 = 42 divide both sides by 3
v + c = 14
by solving the system of equations:
v - c = 6
v + c = 14
we find
v = 10 mph
c = 4 mph
click here to see the step by step solution of the system of equations:
the speed of the boat in still water is 10 mph.