Question

If a car travels 40% of the total distance with a speed $v_1$, then the remaining distance with the car is
Identify the correct option from the following:

• A. $\frac{1}{2} v_1 v_2$
• B. $\frac{v_1 + v_2}{2}$
• C. $\frac{2 v_1 v_2}{v_1 + v_2}$
• D. $\frac{5 v_1 v_2}{3 v_1 + 2 v_2}$

Hint:

To find the average speed over different segments, use the formula $v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}}$, accounting for the time taken for each segment.

Answer 1

The Correct Option is D

Step 1: Interpret the problem
The question seems incomplete; assume it asks for the average speed. Total distance $d$, 40% at speed $v_1$ (distance $0.4d$), remaining 60% at speed $v_2$ (distance $0.6d$). Step 2: Compute the average speed
Time for first part: $t_1 = \frac{0.4d}{v_1}$. Time for second part: $t_2 = \frac{0.6d}{v_2}$. Total time: $t = t_1 + t_2 = \frac{0.4d}{v_1} + \frac{0.6d}{v_2}$. Average speed: $v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} = \frac{d}{\frac{0.4d}{v_1} + \frac{0.6d}{v_2}}} = \frac{1}{\frac{0.4}{v_1} + \frac{0.6}{v_2}}} = \frac{v_1 v_2}{0.4 v_2 + 0.6 v_1} = \frac{5 v_1 v_2}{2 v_1 + 3 v_2} = \frac{5 v_1 v_2}{3 v_1 + 2 v_2}$. Step 3: Match with options
The average speed $\frac{5 v_1 v_2}{3 v_1 + 2 v_2}$ matches option (4).