Chapter 6.5, Problem 22PPS

To determine

To determine the speed of Malik and Julio in still water

Answer to Problem 22PPS

6.07 miles per hour

Explanation of Solution

Given:

	Time travelled against the current(in hours)	Time travelled with the current(in hours)
Malik	2	1
Julio	2.5	1.5

Total distance travelled against the current: 9.5 miles

Total distance travelled with the current: 20.5 miles

Speed of the current: 3 miles per hour.

Formula used:

  $Speed=\frac{Distance}{Time}$

Speed in still water = speed of the current + speed of canoe still water

Calculation:

Let x be the distance travelled against the current.

Let y be the distance travelled with the current.

From the table,

  $2x+2.5y=\mathrm{9.5....................}(1)$

  $x+1.5y=\mathrm{20.5....................}(2)$

Multiply equation (2) with 2,

  $\Rightarrow 2x+3y=\mathrm{41....................}(3)$

Subtract equation (2) from equation (3),

  $\begin{array}{l}\Rightarrow (2x+3y)-(2x+2.5y)=41-9.5\\ \Rightarrow 0.5y=31.5\\ \Rightarrow y=63\end{array}$

Substitute the value of y in equation (2),

  $\begin{array}{l}\Rightarrow x+1.5(63)=20.5\\ \Rightarrow x=-74\end{array}$

The distance travelled with the current is 63 miles

Total time travelled with the current is 20.5 miles

  $Speed=\frac{63}{20.5}=3.07$

Speed in still water = 3.07 + 3 = 6.07 miles per hour.

Conclusion:

Therefore, the speed of Malik and Julio in still water is 6.07 miles per hour.