Question 761617
Distance = Rate x Time
{{{D = R*T}}}
Solve the equation for T by dividing both sides by R
{{{T = D/R}}}
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Let C = the rate of the water current.
The downstream rate is then 8mph + C
and the upstream rate is 8mpH - C.
Since T (The time), is the same in both the upstream and downstream equations, you can set the Distance/Rate ratio equal to each other and solve for C
{{{22/(8 + C) = 10/(8 - C)}}}
Multiply both sides by (8+C) and (8-C).
{{{(22/cross((8 + C)))*cross((8+C))*(8-C) = (10/cross((8 - C)))*(8+C)*cross((8-C))}}}
Simplify
{{{22*(8-C) = 10*(8+C)}}}
Multiply through.
{{{176 - 22C = 80 + 10C}}}
Add 22C to both sides.
{{{176 = 80 + 32C}}}
Subtract 80 from both sides.
{{{96 = 32C}}}
Divide both sides by 32.
{{{highlight(3 = C)}}}
The current of the water is 3mph