Question 236320
rate * time = distance.


the rate is a combination of the boat and the stream.


with the stream, the rate is (b+s)


against the stream, the rate is (b-s)


b is the rate of the boat
s is the rate of the stream.
h is the time in hours.
d = distance


going downstream, the formula for rate * time = distance becomes:


(b+s) * 2 = 36 (equation 1)


coming back up stream, the formula for rate * time = distance becomes:


(b-s) * 3 = 36 (equation 2)


since both these formulas are equal to 36, then they both must be equal to each other, so we have:


(b+s) * 2 = (b-s) * 3


remove parentheses to get:


2b + 2s = 3b - 3s


subtract 2b and add 3s to both sides of this equation to get:


3s + 2s = 3b - 2b which becomes:


5s = b


replace b with 5s in equation 1 to get:


(b+s) * 2 = 36 (equation 1) becomes:


(5s+s) * 2 = 36 which becomes


6s * 2 = 36 which becomes:


12s = 36 which becomes


s = 3


you have:


s = 3
b = 5s = 5*3 = 15


replace s and b in both original equations to confirm the answers are good for both equations.


both original equations are:


(b+s) * 2 = 36 (equation 1)
(b-s) * 3 = 36 (equation 2)


replace b with 15 and s with 3 to get:


(15+3) * 2 = 36 (equation 1)
(15-3 * 3 = 36 (equation 2)


these equations bgecome:


18*2 = 36
12*3 = 36


since both equations are true, the answer is confirmed.


your answer is:


rate of the boat is 15 miles per hour.
rate of the stream is 3 miles per hour.