91Ó°ÊÓ

62 miles downstream in a motor boat .

27 miles downstream on a jet ski.

Speed on the jet ski was 10 mph faster than in the motor boat.

Bill spent a total of 4 hours on the water.

Let the rate of speed in the motor be x .

$$\begin{gathered} Speed=\frac{Dis\tan ce}{Time} \\ Time=\frac{Dis\tan ce}{Speed} \end{gathered}$$

Time Taken in downstream in a motor boat $=\frac{62}{x}$

Time Taken in downstream on a jet ski$=\frac{27}{x+10}$

The value of total time is 4 hours .

Therefore, The equation is :-

$\frac{62}{x}+\frac{27}{x+10}=4$

Solving the equation:-

$$\begin{gathered} \frac{62}{x}+\frac{27}{x+10}=4 \\ 62(x+10)+27x=4x(x+10) \\ 62x+620+27x=4x^2+40x \\ 4x^2-49x-620=0 \end{gathered}$$

Solving the quadratic equation , we get:-

$$\begin{gathered} x_{1, 2}=\frac{-\left(-49\right)Â\pm \sqrt{{\left(-49\right)}^2-4· 4\left(-620\right)}}{2· 4} \\ {x}_{1, 2}=\frac{-\left(-49\right)Â\pm  111}{2· 4} \\ {x}_1=\frac{-\left(-49\right)+111}{2· 4}, x_2=\frac{-\left(-49\right)-111}{2· 4} \\ x=20, x=-\frac{31}{4} \end{gathered}$$

Since, Negative value of speed have no sense. Therefore, The rate of speed in the motor boat is 20 mph .