Problema Solution
Jill can kayak downstream a distance of 20 kilometers in 2 hours. Going upstream, she can kayak a distance of only 18 kilometers in 3 hours. How fast could Jill kayak in still water (if there were no current)?
Answer provided by our tutors
let
k = the rate of the kayak in still water
c = the rate of the current
t1 = 2 hr the time of the travel with the current
d1 = 20 km the distance downstream
t2 = 3 hr the time of the travel against the current
d2 = 18 km the distance upstream
the rate of the kayak traveling upstream is: k - c
the rate of the kayak traveling downstream is: k + c
since the rate = distance/time => distance = time*rate
traveling downstream
d1 = t1(k + c)
t1(k + c) = d1
2(k + c) = 20 divide both sides by 2
k + c = 10
traveling upstream
d2 = t2(k - c)
t2(k - c) = d2
3(k - c) = 18 divide both sides by 3
k - c = 6
we have the following system
k + c = 10
k - c = 6
by solving we find
k = 8 mph
c = 2 mph
click here to see the step by step solution of the system of equations
the speed of the kayak in still water is 8 mph.