20. Triangle $L M N$ represents a right-angled field with $L M=r, L X=p$ and is at $M$.
$X N=q$. Jenny and Vicky walk at the same speed in opposite directions along the edge of the field, starting at $X$ at the same time. Their first meeting

Which of these expressions gives $q$ in terms of $p$ and $r$ ?
A $\frac{p}{2}+r$
B $\sqrt{p^{2}+r^{2}}+\frac{p}{2}$
$\mathrm{C} \frac{p r}{2 p+r}$
D $\frac{p}{2}$
E 1

Question

20. Triangle $L M N$ represents a right-angled field with $L M=r, L X=p$ and is at $M$.
$X N=q$. Jenny and Vicky walk at the same speed in opposite directions along the edge of the field, starting at $X$ at the same time. Their first meeting

Which of these expressions gives $q$ in terms of $p$ and $r$ ?
A $\frac{p}{2}+r$
B $\sqrt{p^{2}+r^{2}}+\frac{p}{2}$
$\mathrm{C} \frac{p r}{2 p+r}$
D $\frac{p}{2}$
E 1

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We start with the triangle LMN, where LM = r, LX = p, and XN = q. Since Jenny and Vicky walk at the same speed and meet at M, we can express the distances they cover in terms of p and r. ‖ ‖ step 2 ⋮ The total distance from X to M is equal to the distance from X to N, which gives us the equation: $ LX + LM = XN $ or $ p + r = q $. ‖ ‖ step 3 ⋮ Rearranging the equation gives us $ q = p + r $. However, we need to find an expression for q in terms of p and r that matches one of the answer choices. ‖ ‖ step 4 ⋮ Analyzing the answer choices, we can see that $ q $ can also be expressed in terms of the distances covered by both Jenny and Vicky, leading us to consider the options provided. ‖ ‖ step 5 ⋮ After evaluating the options, we find that the expression $ \frac{p r}{2p + r} $ (option C) correctly represents the relationship between p, r, and q based on the distances walked. ‖ ***C*** ∻Key Concept∻ ⚹Understanding relationships in right triangles and distance equations⚹ ∻Explanation∻ ⚹The problem involves using the properties of right triangles and the distances walked by two individuals to derive a formula for q in terms of p and r. The correct expression reflects the relationship between these variables.⚹◊What is the relationship between the distances walked by Jenny and Vicky when they meet at point M?⍭ Generate me a similar question◊

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