Question

Dirk and Steve both plan to run to 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, Dirk has 20 signatures, but Steve just started and doesn't have any yet. Kirk is collecting signatures at an average rate of 6 per hour, while Steve can get 10 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

Answer: 2.5 hours

Explanation:

Let's call the number of signatures that Steve needs to collect "x". We know that Dirk has 20 signatures, so he needs to collect "x - 20" more signatures to have the same number as Steve.

We can set up an equation to represent this:

6h + 20 = 10h + x - 20

Simplifying this equation, we get:

x = 4h + 40

So, Steve needs to collect 4 signatures more per hour than Dirk to eventually collect the same number of signatures. We can solve for "h", the number of hours it will take for them to have the same number of signatures:

6h + 20 = 10h + (4h + 40)

6h + 20 = 14h + 40

8h = 20

h = 2.5

So, it will take 2.5 hours for Dirk and Steve to have collected the same number of signatures.