An athlete running on a track falls short of the finish line by 10 m when she runs at a constant speed for a given time. If she increases her speed by 20%, she overshoots by 20 m in the same time. What is the length of the track? 

Concept:

The fundamental formula for motion is, Distance=Speed×Time

Explanation: 

Let d be the length of the track (what we are trying to find), v be her normal speed and t be the time she runs.

At normal speed, the distance covered is d - 10, so \(v \cdot t = d - 10 \quad \text{(Equation 1)}\)

When she increases her speed by 20%, her new speed is 1.2v , and she covers a distance of  d + 20, so:

\(1.2v \cdot t = d + 20 \quad \text{(Equation 2)}\)

⇒ \(v \cdot t = d - 10\)

⇒ \(1.2v \cdot t = d + 20\)

⇒\(1.2(d - 10) = d + 20\)

⇒ \(1.2d - 12 = d + 20\)

⇒ \(1.2d - d = 20 + 12\)

⇒ \(0.2d = 32\)

⇒ \(d = \frac{32}{0.2} = 160 \, \text{meters}\)

Hence, the correct option is 3).