Write an Equation for this graph?

Question

During the swimming of a 50-yard spring in a 25-yard pool, the racers swim away from the starting line and then return to it. Suppose that Alex takes 24 seconds to complete the race. Let "y" stand for the distance from Alex to the starting line when the race is "t" secons old. Make a grpah of y versus t, and write and equation for this grpah

Answer 1

Well, the simplest way would be to assume that Alex swims at a constant speed and takes no time at the turnaround. The resulting graph would be two straight lines - one from the origin to (12, 25) and one from there back to the x-axis (the t-axis) at (24, 0). You'd need two equations.

For the first, the slope will be 25/12 (25 yards in twelve seconds), so the equation would be

y = (25/12)x where 0 <= x <= 12

(You can replace the x with t, if you prefer.)

The other line would have a slope -25/12 (25 yards back in the remaining 12 seconds). We'll have to use the point/slope form for that one:

y - y1 = m(x - x1) using m = -25/12 and the point (24, 0)

y - 0 = (-25/12)(x - 24)

y = (-25/12)x + 50

Again, you can replace x with t.

Hope that helps.

Answer 2

assuming you meant 'sprint'
the graph would look a bit like an upside down 'V'
assuming a constant velocity, the apex of the v would be at 12 secs
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