Problema Solution
A jet-ski can travel comfortably across calm water at 14 mph. If a rider traveled 8 mi down a river in the same amount of time it took to travel 6 mi back up the river, find the rate of the river's current.
Answer provided by our tutors
let
v = 14 mph the jet-ski's speed in calm water
c = the rate of the river's current
d1 = 8 miles the riders distance traveled down a river
d2 = 6 miles the riders distance traveled up the river
t = the time he needs to travel 8 miles down a river = the time he needs to travel 6 miles up the river
downstream speed: v + c
upstream speed: v - c
since speed = distance/time => distance = speed*time
d1 = (v + c)t
(v + c)t = d1
(14 + c)t = 8 => t = 8/(14 + c)
d2 = (v - c)t
(v - c)t = d2
(14 - c)t = 6
lets plug t = 8/(14 + c) in the above equation
(14 - c)*8/(14 + c) = 6
by simplifying and solving the equations we find
c = 2mph
click here to see the step by step solution of the equation
the rate of the river's current is 2 mph.