Question

Isaac and Haley both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Isaac has 30 signatures, but Haley just started and doesn't have any yet. Isaac is collecting signatures at an average rate of 5 per hour, while Haley can get 8 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many hours will have gone by?

Answer 1

It will take 10 hours for Isaac and Haley to have collected the same number of signatures when Isaac collects at a rate of 5 per hour and Haley at a rate of 8 per hour, with Isaac starting with 30 signatures.

Step-by-step explanation:

To find out when Isaac and Haley will have the same number of signatures, we can set up an equation. Let's denote the number of hours it takes for them to have the same number of signatures as h. Since Isaac starts with 30 signatures, his total number of signatures after h hours will be 30 + 5h because he collects signatures at a rate of 5 per hour. Haley starts with 0 signatures and collects them at a rate of 8 per hour, so her total after h hours will be 8h.

The point at which both have the same number of signatures would be when these two expressions are equal:

30 + 5h = 8h

We can solve for h by subtracting 5h from both sides to get:

30 = 3h

Now, dividing both sides by 3 gives us:

h = 10

Therefore, it will take 10 hours for both Isaac and Haley to have the same number of signatures if they continue collecting at their current rates.