Problema Solution
A motorboat traveling a distance of 150 miles in 3 hours while traveling with the current. Against the current, the same trip took 5 hours. Find the rate of the boat in calm water and the rate of the current.
Answer provided by our tutors
et
v = the boats speed in still water, v>0
c = the speed of the current
d = 150 miles
t1 = 3 hr the time traveling downstream (with the current)
t2 = 5 hr the time traveling upstream (against the current)
downstream speed: v + c
upstream speed: v - c
since speed = distance/time
v + c = d/t1
v + c = 150/3
v + c = 50
v - c = d/t2
v - c = 150/5
v - c = 30
by solving the system of equations
v + c = 50
v - c = 30
we find
v = 40 mph
c = 10 mph
click here to see the step by step solution of the system of equations
the rate of the boat in calm water is 40 mph and the rate of the current os 10 mph.