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Christopher is a graphic designer who creates business websites. It takes him 2.4 hours to complete one website page. He finds out about a new software program that will cut his time in half for completing one page, but it will take him 15 hours to learn the new program.

Which equation can be used to find the number of website pages, x, that Christopher needs to create so that his time spent using the new program will be the same as his current time?

How many website pages would Christopher need to create in order to save time using the new software program?

1 answer

To determine when the time spent using the new program equals the time spent using the old method, we can set up an equation based on the time spent on each method.

  1. Current Method:

    • Time to complete one page: 2.4 hours
    • Time to complete \( x \) pages: \( 2.4x \) hours

  2. New Program:

    • Time to learn the program: 15 hours
    • Time to complete one page with the program (which cuts the time in half): \( \frac{2.4}{2} = 1.2 \) hours
    • Time to complete \( x \) pages with the program: \( 15 + 1.2x \)

  3. Setting up the equation: We want the total time spent on the current method to equal the total time spent on the new program:

    \[ 2.4x = 15 + 1.2x \]

  4. Solving for \( x \): \[ 2.4x - 1.2x = 15 \] \[ 1.2x = 15 \] \[ x = \frac{15}{1.2} = 12.5 \]

Since Christopher can't create half a page, he would need to complete at least 13 pages to start saving time by using the new program.

Therefore, the final answers are:

  • The equation is: \( 2.4x = 15 + 1.2x \)
  • Christopher needs to create 13 pages to save time using the new software program.