Chapter 2, Problem 58A

To determine

To Calculate:The difference in time elapsed to cover the same distance at difference speeds.

Answer to Problem 58A

  $1.8\min$

Explanation of Solution

Given:

Your speed, $v_1=90.0\text{km/h}$

Friend’s speed, $v_2=95.0\text{km/h}$

Distance covered, $d=50.0\text{km}$

Formula Used:

Time elapsed can be obtained by:

  $t=\frac{d}{v}$

Where, v is the speed and dis the distance covered.

Calculations:

Substitute the values in above formula and calculate the time elapsed.

  $\begin{array}{c}{t}_1=\frac{d}{v_1}\\ =\frac{50\text{km}}{\text{90}\text{km/h}}\\ =0.56\text{h}\\ =0.56\times 60\min \\ =33.6\min \end{array}$

  $\begin{array}{c}{t}_2=\frac{d}{v_2}\\ =\frac{50\text{km}}{\text{95}\text{km/h}}\\ =0.53\text{h}\\ =0.53\times 60\min \\ =31.8\min \end{array}$

The difference in the time is:

  $\begin{array}{c}\Delta t=t_2-t_1\\ =33.6\min -31.8\min \\ =1.8\min \end{array}$

Conclusion:

Thus, the friend would finish the trip sooner by $1.8$ minutes.