Question

leila is walking from the park at point p to a restaurant at point r. she wants to stop for a break when the distance she has traveled and the distance she has left to travel has a ratio of 3:5. at which point should leila stop for her break?

Explanation:

Step1: Let the total distance be \(d = PR\), the distance traveled be \(x\) and the distance left be \(y\).

We know that \(\frac{x}{y}=\frac{3}{5}\), and also \(x + y=d\).

Step2: Express \(y\) in terms of \(x\) from the ratio.

From \(\frac{x}{y}=\frac{3}{5}\), we get \(y=\frac{5}{3}x\).

Step3: Substitute \(y\) into the sum - equation.

Substitute \(y=\frac{5}{3}x\) into \(x + y=d\), we have \(x+\frac{5}{3}x=d\). Combining like - terms gives \(\frac{3x + 5x}{3}=d\), or \(\frac{8x}{3}=d\), so \(x=\frac{3}{8}d\).
This means Leila should stop at a point that is \(\frac{3}{8}\) of the way from \(P\) to \(R\).

Answer:

Leila should stop at a point that is \(\frac{3}{8}\) of the total distance from \(P\) to \(R\).