Question

4.) oliver can ride his bike for 40 minutes and travel 12 miles.
a.) write the fraction that represents his given constant speed.
b.) write the fraction that represents how many minutes x he can ride in 29 miles.
c.) write a proportion using the fractions from parts (a) and (b) to determine how long itll take oliver to ride his bike in 29 miles. round your answer to the nearest hundredths place.
d.) write a two variable equation to represent how many miles he can ride his bike in any time interval.

Explanation:

Part (a)

Step1: Recall speed formula

Speed is distance over time. Here, distance is 12 miles, time is 40 minutes.
$\frac{\text{Distance}}{\text{Time}} = \frac{12}{40}$

Step1: Define the fraction

We want time (x minutes) over distance (29 miles) to set up proportion later. So the fraction is $\frac{x}{29}$.

Step1: Set up proportion

From part (a), speed is $\frac{12}{40}$, from part (b), the ratio is $\frac{x}{29}$. Since speed is constant, $\frac{12}{40}=\frac{x}{29}$.

Step2: Solve for x

Cross - multiply: $12\times29 = 40x$. Then $x=\frac{12\times29}{40}$. Calculate $12\times29 = 348$, so $x=\frac{348}{40}=8.7$. Wait, no, wait: Wait, $\frac{12}{40}=\frac{x}{29}\Rightarrow x=\frac{40\times29}{12}$. Let's recalculate: $40\times29 = 1160$, $1160\div12\approx96.67$.
Wait, I made a mistake earlier. The speed is distance over time, so the proportion should be $\frac{\text{Distance}_1}{\text{Time}_1}=\frac{\text{Distance}_2}{\text{Time}_2}$. So $\frac{12}{40}=\frac{29}{x}$? No, no. Wait, part (a) is $\frac{\text{Distance}}{\text{Time}}=\frac{12}{40}$, part (b) is $\frac{\text{Time}_2}{\text{Distance}_2}=\frac{x}{29}$. Since speed is constant, $\frac{\text{Distance}}{\text{Time}}=\frac{\text{Distance}_2}{\text{Time}_2}$? No, speed is $\frac{D}{T}$, so if we have $\frac{12}{40}=\frac{29}{x}$ (where x is time for 29 miles), then $12x = 40\times29$, $x=\frac{40\times29}{12}=\frac{1160}{12}\approx96.67$.

Answer:

$\frac{12}{40}$ (or simplified as $\frac{3}{10}$)

Part (b)