14. an object travels along a horizontal straight path at a constant rate. the object travels \\( \\frac { 1…

14. an object travels along a horizontal straight path at a constant rate. the object travels \\( \\frac { 1 } { 25 } \\) of the length of the path in \\( \\frac { 4 } { 5 } \\) second. at that rate, how many seconds does it take the object to travel the entire length of the path?\n15. an object travels along a horizontal straight path at a constant rate. the object travels \\( \\frac { 1 } { 20 } \\) of the length of the path in \\( \\frac { 3 } { 5 } \\) second. at that rate, how many seconds does it take the object to travel the entire length of the path?\n16. ron was painting decorations for a party. he painted for 10 minutes and painted \\( 3 \\frac { 1 } { 2 } \\) decorations. at what rate, in decorations per hour, is he painting?\n17. leslie was downloading files on her computer at work. in 20 minutes she downloaded \\( 15 \\frac { 1 } { 2 } \\) files. at what rate, in files per hour, is she downloading?

14. an object travels along a horizontal straight path at a constant rate. the object travels \\( \\frac { 1 } { 25 } \\) of the length of the path in \\( \\frac { 4 } { 5 } \\) second. at that rate, how many seconds does it take the object to travel the entire length of the path?\n15. an object travels along a horizontal straight path at a constant rate. the object travels \\( \\frac { 1 } { 20 } \\) of the length of the path in \\( \\frac { 3 } { 5 } \\) second. at that rate, how many seconds does it take the object to travel the entire length of the path?\n16. ron was painting decorations for a party. he painted for 10 minutes and painted \\( 3 \\frac { 1 } { 2 } \\) decorations. at what rate, in decorations per hour, is he painting?\n17. leslie was downloading files on her computer at work. in 20 minutes she downloaded \\( 15 \\frac { 1 } { 2 } \\) files. at what rate, in files per hour, is she downloading?

Answer

Explanation:

Step1: Convert minutes to hours

Since (1) hour ( = 60) minutes, (10) minutes (=\frac{10}{60}=\frac{1}{6}) hour.

Step2: Set up a proportion for the rate

Let (r) be the rate (decorations per hour). We know that rate (r=\frac{\text{number of decorations}}{\text{time (in hours)}}). Given the number of decorations (n = 3\frac{1}{2}=\frac{7}{2}) and time (t=\frac{1}{6}) hour. Using the formula (r=\frac{n}{t}), we substitute the values: (r=\frac{\frac{7}{2}}{\frac{1}{6}}).

Step3: Simplify the division of fractions

When dividing by a fraction, we multiply by its reciprocal. So (r=\frac{7}{2}\times6). [ \begin{align*} r&=\frac{7\times6}{2}\ &= 21 \end{align*} ]

Answer:

(21) decorations per hour