What is the speed of the boat in still water? Statement I: The ratio of downstream speed to upstream speed is <span class="math-inline" data-latex-source="16:9" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mo>:</mo><mn>9</mn></mrow><annotation encoding="application/x-tex">16:9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">9</span></span></span></span></span>. Statement II: The boat covers <span class="math-inline" data-latex-source="80" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn></mrow><annotation encoding="application/x-tex">80</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">80</span></span></span></span></span> km downstream in <span class="math-inline" data-latex-source="2.5" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn></mrow><annotation encoding="application/x-tex">2.5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.5</span></span></span></span></span> hours. Choose the standard data-sufficiency option.
Practice this question from Chapter Mock 16: Data Sufficiency, with options and an explanation.
Question
What is the speed of the boat in still water?
Statement I: The ratio of downstream speed to upstream speed is <span class="math-inline" data-latex-source="16:9" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mo>:</mo><mn>9</mn></mrow><annotation encoding="application/x-tex">16:9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">9</span></span></span></span></span>.
Statement II: The boat covers <span class="math-inline" data-latex-source="80" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn></mrow><annotation encoding="application/x-tex">80</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">80</span></span></span></span></span> km downstream in <span class="math-inline" data-latex-source="2.5" data-display-mode="false" contenteditable="false"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn></mrow><annotation encoding="application/x-tex">2.5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.5</span></span></span></span></span> hours.
Choose the standard data-sufficiency option.
Option A
A
Option B
B
Option C — Correct answer
C
Correct choice.
Option D
D
Option E
E
Explanation
Statement I alone gives only a ratio. Statement II alone gives only downstream speed $=80\div2.5=32$ km/h. Together, downstream and upstream are $16k$ and $9k$, so $16k=32$ gives $k=2$ and upstream $=18$. Still-water speed $=\frac{32+18}{2}=25$ km/h. So the answer is C.