r = rate of current

10 + r = speed of boat going downstream {with the current}

10 - r = speed of boat going upstream {against the current}

t = time in hours going downstream

t + 3 = time in hours going upstream

distance = rate x time

*Upstream*d = 70

rate = 10 - r

time = t + 3

70 = 10t + 30 - rt - 3r {distance = rate x time}

70 = 10t - rt + 30 - 3r {re-arranged}

70 = t(10 - r) + 30 - 3r {factored t out of first two terms}

t(10 - r) = 3r + 40 {subtracted 30 and added 3r}

3r + 40

---------- = t {divided each side by (10 - r)

10 - r

*Downstream*d = 70

r = 10 + r

t = t

70 = (10 + r)(t) {distance = rate x time}

70

-------- = t {solved for t}

10 + r

3r + 40 70

---------- = -------- {both were equal to t, so set them equal to each other}

10 - r 10 + r

30r + 3r² + 400 + 40r = 700 - 70r {cross-multiplied}

3r² + 70r + 400 = 700 - 70r {combined like terms}

3r² + 140r - 300 = 0 {subtracted 700 and added 70r}

r ≈ 2.05 {used quadratic formula and rounded}

**rate of current is approximately 2.05 mph***- Algebra House*
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