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Students in Miss Moseley's fourth grade class are learning multiplication, and they demonstrate mastery by passing assessments. Travis has passed 11 tests, and his classmate, Jenifer, has passed 2 tests. Going forward, Travis plans to pass 2 tests per week. Meanwhile, Jenifer plans to pass 5 tests per week. Eventually Jenifer will catch up to Travis. When the number of tests each student has passed are equal, how many tests will each student have passed and how many weeks will it take?

1 answer

To determine when Jenifer will catch up to Travis, we need to establish the number of tests they will have passed after a certain number of weeks.

Let:

  • \( T \) represent the number of tests Travis has passed,
  • \( J \) represent the number of tests Jenifer has passed,
  • \( w \) be the number of weeks after the current point.

Initial tests passed:

  • Travis: \( 11 \)
  • Jenifer: \( 2 \)

Tests passed per week:

  • Travis: \( 2 \)
  • Jenifer: \( 5 \)

After \( w \) weeks, the number of tests passed by each student can be expressed as: \[ T = 11 + 2w \] \[ J = 2 + 5w \]

We need to find \( w \) such that \( T = J \): \[ 11 + 2w = 2 + 5w \]

Now, we will solve for \( w \):

  1. Rearrange the equation: \[ 11 - 2 = 5w - 2w \] \[ 9 = 3w \]
  2. Divide by 3: \[ w = 3 \]

Now that we have \( w = 3 \), we will calculate the total number of tests each student has passed after 3 weeks.

For Travis: \[ T = 11 + 2 \cdot 3 = 11 + 6 = 17 \]

For Jenifer: \[ J = 2 + 5 \cdot 3 = 2 + 15 = 17 \]

Thus, after 3 weeks, both Travis and Jenifer will have passed 17 tests.

In conclusion:

  • The number of tests each student has passed when Jenifer catches up to Travis is \( \boxed{17} \).
  • The number of weeks it takes for Jenifer to catch up is \( \boxed{3} \).