Question
If a car covers $${\frac{2}{5}^{th}}$$ of the total distance with $${v_1}$$ speed and $${\frac{3}{5}^{th}}$$ distance with $${v_2}$$ then average speed is
A.
$$\frac{1}{2}\sqrt {{v_1}{v_2}} $$
B.
$$\frac{{{v_1} + {v_2}}}{2}$$
C.
$$\frac{{2{v_1}{v_2}}}{{{v_1} + {v_2}}}$$
D.
$$\frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}}$$
Answer :
$$\frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}}$$
Solution :
Average speed $$ = \frac{{{\text{Total distance travelled}}}}{{{\text{Total time taken}}}}$$
$$\eqalign{
& = \frac{x}{{\frac{{\frac{{2x}}{5}}}{{{v_1}}} + \frac{{\frac{{3x}}{5}}}{{{v_2}}}}} \cr
& = \frac{{5{v_1}{v_2}}}{{3{v_1} + 2{v_2}}} \cr} $$