Question

Jake and Sergio are planting tulip bulbs Jake has planted 60 bulbs and is planting at a rate of 44 bulbs per hour Sergio has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jake and Sergio have planted the same number of bulbs? What number of bulbs will this be? Write and solve an equation to determine the answer.

Answer 1

Jake and Sergio will have planted the same number of bulbs after 3 hours, which will total to 192 bulbs each.

Step-by-step explanation:

Jake and Sergio are planting tulip bulbs at different initial counts and rates. To find when they will have planted the same number of bulbs, we can set up an equation where the number of bulbs Jake plants is equal to the number Sergio plants.

Let h be the number of hours they continue planting. Jake starts with 60 bulbs and plants at a rate of 44 bulbs per hour. Sergio starts with 96 bulbs and plants at a rate of 32 bulbs per hour.

Jake's bulbs: 60 + 44h
Sergio's bulbs: 96 + 32h

Setting these equal gives us the equation:
60 + 44h = 96 + 32h

To solve for h, we subtract 32h from both sides and then subtract 60 from both sides to get:
12h = 36

Dividing both sides by 12 gives us:
h = 3

After 3 hours, they will have planted the same number of bulbs. To find that number, we substitute h back into either of Jake or Sergio's equations:

Jake's bulbs after 3 hours: 60 + 44(3) = 60 + 132 = 192 bulbs
Sergio's bulbs after 3 hours: 96 + 32(3) = 96 + 96 = 192 bulbs