Question

nathan on his bike
use the information below to answer the following questions.
as nathan rode his bicycle up a hill, he had a friend record the distance he traveled from the bottom of the hill at various points in time. unfortunately, his friend forgot to record some of the data, so two of the entries, x and y, are incomplete. the times and distances that his friend did record are shown in the table below.

time in seconds (t)	distance traveled in feet (d)
5	y
x	54
14	84

after nathan reached the top of the hill, he rode 1/6 mile in 2/3 minute on level ground, then rode 1/4 mile in 3/8 minute downhill, and then rode 1/8 mile in 3/4 minute on level ground again. at what rate was nathan traveling during each of these distances?
match each rate to its equivalent unit by clicking the circle on the left and dragging the line to the matching answer.
1/6 mile in 2/3 minute
1/4 mile in 3/8 minute
1/8 mile in 3/4 minute
1/6 miles per minute
1/4 miles per minute
2/3 miles per minute

Explanation:

Step1: Calculate speed for first - given rate

To find the speed when traveling $\frac{1}{6}$ mile in $\frac{2}{3}$ minute, use the formula speed = $\frac{\text{distance}}{\text{time}}$. So, speed = $\frac{\frac{1}{6}}{\frac{2}{3}}=\frac{1}{6}\times\frac{3}{2}=\frac{1}{4}$ miles per minute.

Step2: Calculate speed for second - given rate

For traveling $\frac{1}{4}$ mile in $\frac{3}{8}$ minute, speed = $\frac{\frac{1}{4}}{\frac{3}{8}}=\frac{1}{4}\times\frac{8}{3}=\frac{2}{3}$ miles per minute.

Step3: Calculate speed for third - given rate

When traveling $\frac{1}{8}$ mile in $\frac{3}{4}$ minute, speed = $\frac{\frac{1}{8}}{\frac{3}{4}}=\frac{1}{8}\times\frac{4}{3}=\frac{1}{6}$ miles per minute.

Answer:

$\frac{1}{6}$ mile in $\frac{2}{3}$ minute matches $\frac{1}{4}$ miles per minute.
$\frac{1}{4}$ mile in $\frac{3}{8}$ minute matches $\frac{2}{3}$ miles per minute.
$\frac{1}{8}$ mile in $\frac{3}{4}$ minute matches $\frac{1}{6}$ miles per minute.