Problema Solution
a boat's crew rowed 10.5 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current covered the same distance, but took 3.5 hours. Find the crews rowing rate in still water and the rate of the current.
Answer provided by our tutors
let
v = the crews rowing rate in still water
c = the rate of the current
t1 = 1.5 hr the time of the trip downstream
t2 = 3.5 hr the time of the return trip upstream
the boats speed downstream: v + c
the boats speed upstream: v - c
a boat's crew rowed 10.5 miles downstream
v + c = 10.5
since the trip upstream and downstream is the same distance
(v + c)*t1 = (v - c)t2
10.5*1.5 = (v - c)*3.5
(v - c)*3.5 = 10.5*1.5 divide both sides by 3.5
v - c = 4.5
by solving the system of equations
v + c = 10.5
v - c = 4.5
we find
v = 7.5 mph
c = 3 mph
click here to see the step by step solution of the system of equations
the crews rowing rate in still water is 7.5 mph.
the rate of the current is 3 mph.