Question

On the windowsill is a plant that is 8 inches tall. It is growing 2 inches per week. A second plant, which is 3 inches tall, is on the coffee table. It is growing 4 inches per week. Eventually the two plants will be the same height. How tall will the plants be?

Answer 1

Both plants will be 13 inches tall when they reach the same height after 2.5 weeks.

Step-by-step explanation:

To determine how tall the plants will be when they are the same height, we can set up an algebraic equation for the plant on the windowsill and the plant on the coffee table. We know the plant on the windowsill is 8 inches tall and growing at a rate of 2 inches per week. This can be represented by 8 + 2t, where 't' is the number of weeks. The plant on the coffee table is 3 inches tall and grows at a rate of 4 inches per week, which can be represented by 3 + 4t. To find out when they will be the same height, we set these two expressions equal to each other:

8 + 2t = 3 + 4t

Solving for 't':

1. Subtract 2t from both sides: 8 = 3 + 2t
2. Subtract 3 from both sides: 5 = 2t
3. Divide both sides by 2: t = 2.5

Now that we know 't', we can find out the height of the plants when they are the same height:

Height of the plant on the windowsill: 8 + 2(2.5) = 13 inches

Height of the plant on the coffee table: 3 + 4(2.5)= 13 inches

So, both plants will be 13 inches tall when they are the same height after 2.5 weeks.

Answer 2

Let's call the height of the first plant as x and the height of the second plant as y.

We know that the first plant is 8 inches tall and growing 2 inches per week, so we can write the equation:

x = 8 + 2t (where t is the time in weeks)

We know that the second plant is 3 inches tall and growing 4 inches per week, so we can write the equation:

y = 3 + 4t

We also know that the two plants will be the same height when they meet, so we can set the two equations equal to each other:

x = y

8 + 2t = 3 + 4t

5 = 2t

t = 2.5

So the plants will be the same height in 2.5 weeks. To find out how tall they will be, we can plug this value of t back into either equation:

x = 8 + 2(2.5) = 8 + 5 = 13 inches

y = 3 + 4(2.5) = 3 + 10 = 13 inches

So both plants will be 13 inches tall when they reach the same height.

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