Alex travels from his house to his friend's house with speed $V_{1}$ and returns to his house with speed $V_{2}$ . The distance between the houses is $X$ . What is the average speed of the Alex?

$\frac{2 V_{1} + V_{2}}{V_{1} + V_{2}}$

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$\frac{V_{1} + 2 V_{2}}{V_{1} V_{2}}$

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$\frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

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$\frac{2 V_{1} V_{2}}{V_{1} + 2 V_{2}}$

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Solution

The correct option is C
$\frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

Distance between the houses = $X$

Speed of onward trip = $V_{1}$

Time taken for onward trip $t_{1}$ = $\frac{X}{V_{1}}$

Speed of return trip = $V_{2}$

Time taken for return trip $t_{2}$ = $\frac{X}{V_{2}}$

To find the average speed,

Total distance travelled = $X + X = 2 X$

Total time = $t_{1} + t_{2}$ = $\frac{X}{V_{1}} + \frac{X}{V_{2}}$

Average speed = $\frac{t o t a l d i s t a n c e t r a v e l l e d}{t o t a l t i m e}$

= $\frac{2 X}{\frac{X}{V_{1}} + \frac{X}{V_{2}}}$

= $\frac{2 X}{X (\frac{1}{V_{1}} + \frac{1}{V_{2}}})$

= $\frac{2}{\frac{V_{1} + V_{2}}{V_{1} V_{2}}}$

= $\frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

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Alex travels from his house to his friend's house with speed V1 and returns to his house with speed V2. The distance between the houses is X. What is the average speed of the Alex?

Alex travels from his house to his friend's house with speed $V_{1}$ and returns to his house with speed $V_{2}$ . The distance between the houses is $X$ . What is the average speed of the Alex?