Question

A red balloon is 40 feet above the ground and rising at a rate of 2 feet per second. At the same time, a blue balloon is 60 feet above the ground and descending at a rate of 3 feet per second. What will the height of the balloons be when they are the same height above the ground?

Answer 1

The red and blue balloons will be at the same height 4 seconds after we start measuring, and at that time they will both be at a height of 48 feet above the ground.

Step-by-step explanation:

To find the height at which the red and blue balloons are at the same height, we can set up an equation. Let's call the time it takes for the balloons to be at the same height as t. The height of the red balloon can be represented as 40 + 2t, and the height of the blue balloon can be represented as 60 - 3t. Setting these two expressions equal to each other, we get:

40 + 2t = 60 - 3t

Adding 3t to both sides and subtracting 40 from both sides, we get:

5t = 20

Dividing both sides by 5, we find that t = 4. So, the balloons will be at the same height 4 seconds after we start measuring.

To find the height at that time, we can substitute t = 4 into either expression. Using the height expression for the red balloon, we get:

40 + 2(4) = 40 + 8 = 48 feet

Therefore, when they are at the same height, both balloons will be 48 feet above the ground.