Lily swims for 5 hours in stream that has a current of 1 mph. she leaves her dock, swims upstream for 2 miles and then swim back to her dock. what is her swimming speed in still water?

Swimming speed in still water is approximately 1.5 mph

Step-by-step explanation:

Given the speed of the current = 1 mph

distance she swims upstream =2 miles,

the total time = 5 hours.

She swam 2 miles upstream against the  current and 2 miles back to the dock with  the current. The formula that relates  distance, time, and rate is

Let x be the speed in still water.

Then  her speed with the current is x + 1, and

her speed against the current is x – 1.

Total time is equal to 2 miles with upstream and 2 miles downstream.

Now Using quadratic formula to solve above equation we get;

Since speed must be positive, Hence speed of still water is about 1.5 miles per hour.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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