Problema Solution
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
Answer provided by our tutors
let
c = the speed of the current, c>=0
v = the speed of the boat in still water, v>0
d = 210 km the distance downstream and back
t1 = 10 hr the time of the downstream trip
t2 = 70 hr the time of the upstream trip
the speed of the boat when moving upstream is: v - c
the speed of the boat when moving downstream is: v + c
since speed = distance/time => distance = time*speed
t1(v + c) = d/2
t2(v - c) = d/2
by solving the equation
10(v + c) = 210/2
70(v - c) = 210/2
we find
v = 6 mph
c = 4.5 mph
click here to see the step by step solution of the system of equations
the speed of the boat in still water is 6 mph.
the speed of the current is 4.5 mph.