a riverboat travels down stream at 16km in 2 hours and returns the same distance upstream in 3 hours. find the

Question

rate of the boat in still water and the rate of the current? please help.

Answer 1

The boat goes 6 2/3 km/hour in still water and
the current is 1 1/3 km/hr

calculations

16 km's in 2 hours

x is the speed of the boat and y is the speed of the current

2 x + 2y =16
x + y = 8

when the boat goes against the current

3x - 3y = 16
x - y = 5 1/3
x = y + 5 1/3

Substitute this second equation value of x into the first

y + 5 1/3 + y = 8
2y + 5 1/3 = 8
2y = 2 2/3
y = 1 1/3

Knowing y you can use either formula to get x

x + y = 8
x + 1 1/3 = 8
x = 6 2/3

Edit: The difference between me and answer 2 is interpreting you wording. You say "at 16 km in 2 hours" it is either "16 km in 2 hours" or "at 16 km per hour in 2 hours"

Answer 2

distance=rate*time
rate of boat =b
rate of current=c
16km=2hours*(b+c)
16km=3hours*(b-c)
(16=2b+2c)*3 becomes 48=6b+6c
(16=3b-3c)*2 becomes 32=6b-6
80=12b add equations together
b=20/3
16=2*(20/3+c)
16=40/3+2c
8/3=2c
c=4/3
16=3(20/3-4/3)
16=3(16/3)
16=16
rate of boat = 16/3 km/h
rate of current = 4/3 km/h

Answer 3

boat speed = b
current speed = c
distance = 32km

time down stream-

time * rate = distance

2hrs * (b + c) = 32km

time up stream-
3hrs * (b-c) = 32km

solve one eqation for c gives you
c = 16 - b

3hrs * (b - (16 - b)) = 32
3 (2b -16) = 32
6b - 48 = 32
b = 13.33 km/hr

c = 16 - 13.33 = 2.67km/hr


hope this helps