Final answer:
Robert and his mom will take a break after they have both completed planting 15 rows each. This will be after 5 hours of work, given Robert's starting point of 10 rows and planting rate, and his mom's starting point of 5 rows and planting rate.
Step-by-step explanation:
The question requires solving a simultaneous equation based on the rates at which Robert and his mom are planting rows of vegetables in their garden. We want to find when Robert and his mom will have planted the same number of rows.
Let's say they will take a break after 't' hours. Robert has already planted 10 rows and plants at a rate of 1 row per hour. So, after 't' hours, Robert will have planted 10 + t rows. His mom has planted 5 rows so far and plants at a rate of 2 rows per hour, which means after 't' hours she will have planted 5 + 2t rows.
To find the time when they will have planted the same number of rows, we set these two expressions equal to each other:
10 + t = 5 + 2t. If we solve this equation, we get t = 5 hours. Thus, they will each have completed 15 rows when they decide to take a break.