Question

Four athletes took part in a relay race. The first, second, and third person ran ${\frac{2}{5}}^{\text{th}},{\frac{1}{6}}^{\text{th}}$ and ${\frac{1}{3}}^{\text{rd}}$ of the total distance, respectively. The fourth person ran 35km to complete the race. What is the total length of the track?

• A. $4\frac{1}{2}\text{km}$
• B. $10\text{km}$
• C. $6\text{km}$
• D. $12\frac{1}{2}\text{km}$

Answer 1

The correct option is C $6\text{km}$

Let the total length of the track be $x$ km.
From the given condition we have,
Total distance traveled $=$ Sum of all the distance traveled by each participant

Total distance traveled $=\frac{2}{5}x+\frac{1}{6}x+\frac{1}{3}x+\frac{3}{5}$
$x=\frac{2}{5}x+\frac{1}{6}x+\frac{1}{3}x+\frac{3}{5}$
$x=\frac{2\times 6}{5\times 6}x+\frac{1\times 5}{6\times 5}x+\frac{1\times 10}{3\times 10}x+\frac{3}{5}$
$x=\frac{12+5+10}{30}x+\frac{3}{5}$
$x=\frac{27}{30}x+\frac{3}{5}$
$x=\frac{9}{10}x+\frac{3}{5}$
$x-\frac{9}{10}x=\frac{3}{5}$
$\frac{1}{10}x=\frac{3}{5}$
$x=\frac{3}{5}\times 10$
$x=6\text{km}$
Total track length is $6\text{km}$