Question

Need help with 5 and 6. Please explain steps. Thanks!!!!

Answer 1

5. Answer: rate of 6 mph + current of 5 mph = 11 mph

Explanation:

Use d = r * t

`\begin {array}l &\underline{time}&\underline{rate}&\underline{distance}&\underline{equation}\\ with&x&r+5&33&x(r+5)=33\\against&6-x&r-5&3&(6-x)(r-5)=3\\\end{array} \\\\\\\text{Solve each equation for x.}\\\\x(r + 5) = 33\qquad \qquad \qquad (6-x)(r-5)=3\\\\.\qquad \quad x=(33)/(r+5)\qquad \qquad \qquad \qquad 6-x=(3)/(r-5)\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad x=-(3)/(r-5)+6`

`\text{Now, set the equations equal to each other and solve for r:}\\\\(33)/(r+5)=-(3)/(r-5)+6\\\\\\(33)/(r+5)=-(3)/(r-5)+(6(r-5))/((r-5))\\\\\\(33)/(r+5)=(6r-33)/(r-5)\\\\\\33(r-5)=(r+5)(6r-33)\\\\\\33r - 165 = 6r^2-3r-165\\\\\\.\qquad \quad 0=6r^2-36r\\\\\\.\qquad \quad 0=6r(r-6)\\\\\\.\qquad \quad 0=6r\quad or\quad 0=r-6\\\\\\.\qquad \quad r=0\quad or\quad r=6\\\\\text{0 mph is an erroneous solution so Karl's rate was 6 mph}`

6. Answer: 5 hours

Explanation:

Use d = r * t. Since they both traveled the same distance, we can set the (rate * time) for each person equal to each other:

Wilbur: rate = 33 and time = x --> equation: 33x

Mary: rate = 55 and time = x - 2 --> equation: 55(x - 2)

33x = 55(x - 2)

33x = 55x - 110

0 = 22x - 110

110 = 22x

5 = x