Tommy and his mom are planting vegetables in their garden. Tommy has finished planting 5 rows of carrots so far and is planting new rows at a rate of 1 row per hour. His mom has finished 2 rows of tomatoes and will continue planting at 2 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?Write a system of equations, graph them, and type the solution.____ rows
Q. Tommy and his mom are planting vegetables in their garden. Tommy has finished planting 5 rows of carrots so far and is planting new rows at a rate of 1 row per hour. His mom has finished 2 rows of tomatoes and will continue planting at 2 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?Write a system of equations, graph them, and type the solution.____ rows
Define Functions: Let's define the number of rows Tommy and his mom have completed as functions of time, t, where t is in hours. Tommy starts with 5 rows and plants 1 more row per hour. His mom starts with 2 rows and plants 2 more rows per hour.
Write Equations: Write the equations for Tommy and his mom. For Tommy: T(t)=5+t. For his mom: M(t)=2+2t.
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.
Solve for t: Solve for t: Subtract t from both sides: 5=2+t. Then subtract 2 from both sides: t=3 hours.
Plug in t: Plug t = 3 back into either equation to find the number of rows completed. Using Tommy's equation: T(3)=5+3=8 rows.