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Vishnu travelled equal distance at speeds of 10 km/hr, 30 km/hr, and 8 km/hr, and took a total of 15.5 minutes to complete. Find the total distance he travelled, in km.
- A1
- B3
- C4
- D2
Answer not set
Discussion 1
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CCommunity
Let he travelled x km at each speed.
Time taken to cover x km at 10 kmph = x/10 hr
Time taken to cover x km at 30 kmph = x/30 hr
Time taken to cover x km at 8 kmph = x/8 hr
Total time taken = 15.5 minutes = 31/120 hr
$(\begin{array}{l}
\Rightarrow \frac{x}{{10}} + \frac{x}{{30}} + \frac{x}{8} = \frac{{31}}{{120}}\\
\Rightarrow \frac{{12x + 4x + 15x}}{{120}} = \frac{{31}}{{120}}
\end{array})$
⇒ 31x = 31
∴ x = 1
∴ Total distance covered in km = 1 + 1 + 1 = 3 km
Time taken to cover x km at 10 kmph = x/10 hr
Time taken to cover x km at 30 kmph = x/30 hr
Time taken to cover x km at 8 kmph = x/8 hr
Total time taken = 15.5 minutes = 31/120 hr
$(\begin{array}{l}
\Rightarrow \frac{x}{{10}} + \frac{x}{{30}} + \frac{x}{8} = \frac{{31}}{{120}}\\
\Rightarrow \frac{{12x + 4x + 15x}}{{120}} = \frac{{31}}{{120}}
\end{array})$
⇒ 31x = 31
∴ x = 1
∴ Total distance covered in km = 1 + 1 + 1 = 3 km