a steamboat travels 9 miles up a river in 3 hours and returns the same distance down the river in 2 hours. find the speed of the boat in still water and the rate of the current.

Answer 1

speed of boat in still water --- x mph
speed of current --- y mph

distance up river = time (rate) = 3(x-y) = 9
3x-3y = 9
x-y=3
distance down river = 2(x+y) = 9
2x+2y=9

multiply first by 2
2x-2y = 6
2x+2y = 9
add them
4x = 15
x = 15/4 = 3.75 mph
then in x-y = 3
3.75-y = 3
y = .75 mph

the boat has a speed of 3.75 mph in still water, and
the current has a speed of .75 mph

check:
speed with the current = 4.5
distance = 2(4.5) = 9
speed against current = 3
distance = 3(3) = 9

Answer 2

The current of a river is 2 miles per hour. A boat travels to a point 8 miles uptream and back in a total of 3 hours. What is the speed of the boat in still water