Theo and Kade worked on a school project together. Theo worked on the project 3 fewer hours than Kade did. Altogether, they worked for a total of 27 hours. How many hours did they each work on the school project?

Question

Theo worked on the project for
hours.
Kade worked on the project for
h

Answer 1

Let \( T \) be the number of hours Theo worked, and let \( K \) be the number of hours Kade worked. According to the problem, we have two equations:

1. \( T = K - 3 \) (Theo worked 3 fewer hours than Kade)
2. \( T + K = 27 \) (Altogether, they worked for 27 hours)

Now, we can substitute the first equation into the second equation:

\[ (K - 3) + K = 27 \]

Combining like terms gives:

\[ 2K - 3 = 27 \]

Next, add 3 to both sides:

\[ 2K = 30 \]

Now, divide by 2:

\[ K = 15 \]

Now that we know Kade worked 15 hours, we can find out how many hours Theo worked:

\[ T = K - 3 = 15 - 3 = 12 \]

Thus, the time worked by each is:

• Theo worked on the project for 12 hours.
• Kade worked on the project for 15 hours.