Pamela rode her bike at a constant rate of 0.1 kilometer per minute. Which table represents y, the number of kilometers Pamela rode her bike in x minutes?

Steps to Solve

1. Identify the relationship between time and distance

Pamela rides at a rate of $0.1$ kilometers per minute. The total distance $y$ in kilometers for a given time $x$ in minutes can be calculated using the formula: $$ y = 0.1x $$

2. Calculate expected distances

We will use the formula to calculate the expected distances for each number of minutes given in the tables.

• For $x = 5$:
  $$ y = 0.1 \times 5 = 0.5 $$

• For $x = 10$:
  $$ y = 0.1 \times 10 = 1.0 $$

• For $x = 15$:
  $$ y = 0.1 \times 15 = 1.5 $$

• For $x = 20$:
  $$ y = 0.1 \times 20 = 2.0 $$

• For $x = 25$:
  $$ y = 0.1 \times 25 = 2.5 $$

3. Compare with the given tables

Now, we compare the calculated distances with the values in each table to find which correctly represents the relationship.

• Table F

  • $x = 5$, $y = 0.1$
  • $x = 10$, $y = 0.1$
  • $x = 15$, $y = 0.1$
  • $x = 20$, $y = 0.1$
  • $x = 25$, $y = 0.1$

  (Incorrect values)

• Table G

  • $x = 5$, $y = 0.5$
  • $x = 10$, $y = 1.0$
  • $x = 15$, $y = 1.5$
  • $x = 20$, $y = 2.0$
  • $x = 25$, $y = 2.5$

  (Correct values)

• Table H

  • $x = 5$, $y = 0.1$
  • $x = 10$, $y = 0.2$
  • $x = 15$, $y = 0.4$
  • $x = 20$, $y = 0.5$
  • $x = 25$, $y = 0.5$

  (Incorrect values)

• Table J

  • $x = 5$, $y = 5.1$
  • $x = 10$, $y = 15.1$
  • $x = 15$, $y = 15.1$
  • $x = 20$, $y = 20.1$
  • $x = 25$, $y = 25.1$

  (Incorrect values)