Question

raman covers one-fourth of his total journey with a speed of v1 m/s and the remaining journey with a speed of v2 m/s find his average speed

Answer 1

Raman covers one-fourth of his total journey with a speed of v1 m/s and the remaining journey with a speed of v2 m/s find his average speed

Solution:

Average velocity is determined by dividing the distance travelled by the time it takes to travel that far:

$$v_{\text{average}} = \frac{\text{distance}}{\text{time}} = \frac{S}{t} = \frac{S}{t_{AB} + t_{BC}}$$ $$\text{distance AB: } t_{AB} = \frac{S_{AB}}{v_1} = \frac{\frac{S}{4}}{v_1} = \frac{S}{4v_1}$$ $$\text{distance BC: } t_{BC} = \frac{S_{BC}}{v_2} = \frac{S - \frac{S}{4}}{v_2} = \frac{3S}{4v_2}$$

(3) and (2) in (1):

$$v_{\text{average}} = \frac{S}{\frac{S}{4v_1} + \frac{3S}{4v_2}} = \frac{S}{\frac{S(v_2 + 3v_1)}{4v_1v_2}} = \frac{4v_1v_2}{v_2 + 3v_1}$$

Answer: average speed is $\frac{4v_1v_2}{v_2 + 3v_1}$