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

**Answers:**

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"

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

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

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