Question

An ant is 1.2cm up a wall and climbs up 1.7cm each second.A second ant is 30cm up the wall and climbs down 1.5cm each second.After how many seconds will the ants be the same height up the wall?

Answer 1

By setting up an equation that equals the height of both ants after the same amount of time, we can solve for time (t). We find that after 9 seconds, the two ants will be at the same height on the wall.

Step-by-step explanation:

The problem posed involves two ants moving at different rates along a wall. To find out after how many seconds the ants will be at the same height on the wall, we need to set up a simple equation. The first ant starts at 1.2 cm and climbs at a rate of 1.7 cm per second. The second ant starts at 30 cm and climbs down at a rate of 1.5 cm per second.

Let's denote the number of seconds it takes for both ants to be at the same height as t. The height of the first ant after t seconds will be 1.2 + 1.7t cm. The height of the second ant after t seconds will be 30 - 1.5t cm. To determine when these two heights are equal, we set up the equation 1.2 + 1.7t = 30 - 1.5t. Now we combine like terms to solve for t:

1.7t + 1.5t = 30 - 1.2

3.2t = 28.8

t = 28.8 / 3.2

t = 9

Therefore, after 9 seconds, both ants will be at the same height on the wall.