The speed v of an object being propelled through water is given by 2P v(P, C) = where P is the power being used to propel the object, C is the drag coefficient, and k is a positive constant. Swimmers can therefore increase their swimming speeds by increasing their power or reducing their drag coefficients. To compare the effect of increasing power versus reducing drag, we need to somehow compare the two in common units. A frequently used approach is to determine the percentage change in speed that results from a given percentage change in power and in drag. If we work with percentages as fractions, then when power is changed by a fraction r (with x corresponding to 100x percent), P changes from P to P+xP. Likewise, if the drag coefficient is changed by a fraction y, then C changes from C to C + yC. Then, the corresponding fractional change in speed is

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