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Tommy and his mom are planting vegetables in their garden. Tommy has finished planting 55 rows of carrots so far and is planting new rows at a rate of 11 row per hour. His mom has finished 22 rows of tomatoes and will continue planting at 22 rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?\newlineWrite a system of equations, graph them, and type the solution.\newline____ rows\newline

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Q. Tommy and his mom are planting vegetables in their garden. Tommy has finished planting 55 rows of carrots so far and is planting new rows at a rate of 11 row per hour. His mom has finished 22 rows of tomatoes and will continue planting at 22 rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?\newlineWrite a system of equations, graph them, and type the solution.\newline____ rows\newline
  1. Define Functions: Let's define the number of rows Tommy and his mom have completed as functions of time, tt, where tt is in hours. Tommy starts with 55 rows and plants 11 more row per hour. His mom starts with 22 rows and plants 22 more rows per hour.
  2. Write Equations: Write the equations for Tommy and his mom. For Tommy: T(t)=5+t T(t) = 5 + t . For his mom: M(t)=2+2t M(t) = 2 + 2t .
  3. Set Equations Equal: Set the equations equal to find when Tommy and his mom have planted the same number of rows. 5+t=2+2t 5 + t = 2 + 2t .
  4. Solve for t: Solve for t: Subtract t from both sides: 5=2+t 5 = 2 + t . Then subtract 22 from both sides: t=3 t = 3 hours.
  5. Plug in t: Plug t = 33 back into either equation to find the number of rows completed. Using Tommy's equation: T(3)=5+3=8 T(3) = 5 + 3 = 8 rows.

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