Flo and Carl each must read a 500-page book. Flo reads one page every minute. Carl reads one page every 50 seconds. Flo starts reading at 1:00, and Carl starts reading at 1:30. When will Carl catch up to Flo?

A) Using \( t \) as the number of minutes after 1:30, set up an equation with the number of pages Flo has read on the left side and the number of pages Carl has read on the right side. Then solve the problem.

To solve this problem, we need to find out when Carl will catch up to Flo in terms of the number of pages read.

Let's first find out how many pages Flo will have read after a certain number of minutes, denoted as 't'. Since Flo reads one page every minute, the number of pages Flo will have read after 't' minutes can be calculated as t.

Next, let's find out how many pages Carl will have read after 't' minutes. Since Carl reads one page every 50 seconds, we need to convert minutes to seconds. There are 60 seconds in a minute, so 50 seconds is equivalent to 50/60 or 5/6 minutes. The number of pages Carl will have read after 't' minutes can be calculated as (5/6)t.

Now, let's set up an equation to represent the situation. We know that Carl starts reading 30 minutes after Flo, so we need to account for this time difference. The number of pages Flo has read after 't' minutes is t, and the number of pages Carl has read after 't' minutes is (5/6)(t + 30).

So, the equation becomes t = (5/6)(t + 30).

To solve this equation, we can multiply both sides by 6 to eliminate the fraction: 6t = 5(t + 30).

Expanding the right side of the equation gives us: 6t = 5t + 150.

Simplifying further, we have t = 150.

Therefore, Carl will catch up to Flo after 150 minutes.

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