SOLUTION: a motor boat travels 36km down stream in 2 hours . in coming back up streams, the trip takes 3 hours. find the rate of the boat in still water and the rate of the current.(solve

Question 236320: a motor boat travels 36km down stream in 2 hours . in coming back up streams, the
trip takes 3 hours. find the rate of the boat in still water and the rate of the current.(solve using linear system)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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