Problema Solution
A motorboat travels 224km in 7 hours going upstream. It travels 294km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer provided by our tutors
let
d1 = 294 km the distance downstream
d2 = 224 km the distance upstream
t = 7 hr the time of the travel in each direction
c = the rate of the current, c>0
v = the rate of the boat in still water, v>0
traveling downstream the speed of the boat is: v + c
traveling upstream the speed of the boat is: v - c
since rate = distance/time we have
v + c = d1/t
v - c = d2/t
we plug the values and get
v + c = 294/7
v + c = 42
v - c = 224/7
v - c = 32
by solving the system of equations
v + c = 42
v - c = 32
we find
v = 37 km/h
c = 5 km/h
click here to see the step by step solution of the system of equations
the rate of the boat is still water is 37 km/h.
the rate of the current is 5 km/h.