SAT Mathematics Practice Test 4

Let ${\mathit{q}}_{\mathit{s}}$ be the dynamic pressure of the slower fluid moving with velocity ${\mathit{v}}_{\mathit{s}}$ ,and let ${\mathit{q}}_{\mathit{f}}$ be the dynamic pressure of the faster fluid moving with velocity ${\mathit{v}}_{\mathit{f}}$ .Then ${\mathit{v}}_{\mathit{f}}=1.5{\mathit{v}}_{\mathit{s}}$.
Given the equation $\mathit{q}=\frac{1}{2}\mathit{n}{\mathit{v}}^2$ substituting the dynamic pressure and velocity of the faster fluid gives ${\mathit{q}}_{\mathit{f}}=\frac{1}{2}\mathit{n}{\mathit{v}}_{\mathit{f}}^2$ Since ${\mathit{v}}_{\mathit{f}}=1.5{\mathit{v}}_{\mathit{s}}$ the expression $1.5{\mathit{v}}_{\mathit{s}}$ can be substituted for ${\mathit{v}}_{\mathit{f}}$ in this equation, giving ${\mathit{q}}_{\mathit{f}}=\frac{1}{2}\mathit{n}{\left(1.5{\mathit{v}}_{\mathit{s}}\right)}^2$ This can be rewritten as ${\mathit{q}}_{\mathit{f}}=\left(2.25\right)\frac{1}{2}\mathit{n}{\mathit{v}}_{\mathit{s}}^2=\left(2.25\right){\mathit{q}}_{\mathit{s}}$.Therefore, the ratio of the dynamic pressure of the faster fluid is $\frac{{\mathit{q}}_{\mathit{f}}}{{\mathit{q}}_{\mathit{s}}}=\frac{2.25{\mathit{q}}_{\mathit{s}}}{{\mathit{q}}_{\mathit{s}}}=2.25$ Either $2.25$ or the equivalent improper fraction $\frac{9}{4}$ may be gridded as the correct answer.