Question

The oxygen consumption (in milliliter per pound per minute) for a person walking at x mph is approximated by the function f(x)=\frac{5}{3} x^{2}+\frac{5}{3} x+10 \quad(0 \leq x \leq 9)whereas the oxygen consumption for a runner at x mph is approximated by the function g(x)=11 x+10 \quad(4 \leq x \leq 9) b. At what speed is the oxygen consumption the same for a walker as it is for a runner? What is the level of oxygen consumption at that speed?

Answer 1

Answer: Speed = 5.6 mph

              Oxygen consumption = 71.6 mL/lb/min

Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:

f(x) = g(x)

$\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10$

Resolving:

$\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0$

$\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0$

$\frac{5}{3}x^{2} - \frac{28x}{3}=0$

$\frac{x}{3}(5x - 28)=0$

$\frac{x}{3} = 0$

x=0

5x - 28 = 0

$x = \frac{28}{5}$

x = 5.6

The speed when the oxygen consuption is the same is 5.6 mph.

For the level of oxygen consumption:

f(5.6) = g(5.6)

g(5.6) = 11*5.6 + 10

g(5.6) = 71.6

The level of oxygen consumption is 71.6 mL/lb/min

Answer 2

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption is 71.6 milliliter per pound per minute

The oxygen consumption for a person walking at x mph is given by,

             $f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10$

The oxygen consumption for a runner at x mph is approximated given by the function,

             $g(x)=11x+10$

To be oxygen consumption same for both walker and runner, both function must be equal.

             $f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph$

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption at that speed is,

             $g(5.6)=11(5.6)+10=71.6$

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