Chapter SH, Problem 6.5MPS

To determine

To find the rate of boat in still water and the rate of current.

Answer to Problem 6.5MPS

The speed of boat in still water is $4.5$ miles per hour and the speed of current be $0.5$ miles per hour.

Explanation of Solution

Given:

The total distance is $10$ miles. The time taken for upstream is $2.5$ hours and time taken for downstream is $2$ hours.

Calculation:

Let the speed of boat in still water be $x$ miles per hour.

And the speed of current be $y$ miles per hour.

So, the upstream speed of boat will be $x+y$ miles per hour.

And the downstream speed of boat will be $x-y$ miles per hour.

The downstream distance $=$ the upstream distance

  $\begin{array}{l}2.5(x-y)=2(x+y)\\ 2.5x-2x-2.5y-2y=0\\ 0.5x-4.5y=0\\ x-9y=0\mathrm{...........}(1)\end{array}$

Also

  $\begin{array}{l}\frac{10}{x+y}=2\\ x+y=\mathrm{5..........}(2)\end{array}$

Now, solving equation (1) and (2) as follows-

  $\begin{array}{l}x-9y=0\mathrm{.........}(1)\\ \underset{\_}{x+y=5\mathrm{..........}(2)}\text{(Subtracting)}\\ -10y=-5\\ y=0.5\\ x=5-0.5\\ x=4.5\end{array}$

Hence, the speed of boat in still water is $4.5$ miles per hour and the speed of current be $0.5$ miles per hour.