Chapter 6, Problem 65A

To determine

Outcome of the race.

Answer to Problem 65A

O wins the race.

Explanation of Solution

Given:

Distance between shore to dock, $d=1.5\text{km}$

Speed of O and Lt, $v_1=4\text{m/s}$

Speed of river, $v_2=2\text{m/s}$

Formula Used:

Time, distance and speed relation is $d=s\times t$ .

Where $d$ is distance, $s$ is speed and $t$ is time.

Calculation:

Total distance that O travels is $d=1.5+1.5=3\text{km}$

So, time taken by O to go and return is

  $\begin{array}{l}t=\frac{3\times {10}^3}{4}\\ =750\text{s}\end{array}$

Now, let Lt is against the current. Time taken by Lt is

  $\begin{array}{l}t=\frac{x_1}{v_1}+\frac{x_2}{v_2}\\ =\frac{1.5\times {10}^3}{4-2}+\frac{1.5\times {10}^3}{4+2}\\ =1000\text{s}\end{array}$

Conclusion:

As time taken by O is less than Lt. So, O wins the race.