# 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

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 Click here to see ALL problems on Mixture Word Problems 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(3464)   (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.