A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Rate of the boat still in water:

Rate of the current:

Let x be rate of boat in still water

let y be rate of current

we use this equation to relate quantities:

distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y

(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y

(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream

144 = 3 (x-y)

144 = 3x - 3y

for downstream

144 = 2 (x+y)

72 = x + y

system of eqns:

144 = 3x - 3y

72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3 (72 - y) - 3y

144 = 216 - 3y - 3y

144 = 216 - 6y

144 - 216 = - 6y

-72 = - 6y

y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h

rate of the current is 12 km/h