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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