Question 426820
A boat goes upstream 600 m, moving 30 m/min through the water. The boat travels back downstream to the starting point, this time only going 20 m/min through the water. The total time spent is 75 minutes. How fast was the current flowing?
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b = boat's speed relative to the water
c = current
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Upstream  + downstream = 75 mins
600/(30 - c) + 600/(20 + c) = 75
One equation and one variable
{{{600(20+c) + 600(30-c) = 75(20+c)(30-c) = 75(600+10c-c^2)}}}
{{{8(20+c) + 8(30-c) = (600+10c-c^2)}}}
{{{160 + 240 = (600+10c-c^2)}}}
{{{c^2 - 10c - 200 = 0}}}
(c-20)*(c+10) = 0
c = 20 m/min