It takes Andy and Ben the same amount of time to eat 1 large piece of chocolate. It takes Charlotte 3 more mins than Andy and Ben to eat the same piece of chocolate. One day, Andy, Charlotte and Ben share 2 pieces of chocolate among them. It takes them 5 mins to eat 2 pieces of chocolate together. Let x represent the time it takes Andy and Ben to eat 1 large piece of chocolate. How long does it take each of them to eat 1 large piece of chocolate?
To solve this problem, we can start with the information given and work our way through the problem step by step.
Let's denote the time it takes Andy and Ben to eat 1 large piece of chocolate as x minutes.
According to the problem, it takes Charlotte 3 more minutes than Andy and Ben to eat the same piece of chocolate. So, Charlotte takes (x + 3) minutes to eat 1 large piece of chocolate.
Now, let's consider the time it takes Andy, Charlotte, and Ben to eat 2 pieces of chocolate together. The problem tells us that it takes them 5 minutes to eat 2 pieces of chocolate.
If Andy takes x minutes to eat 1 large piece of chocolate, then in 5 minutes, he would eat 5/x pieces of chocolate.
Similarly, Ben would also eat 5/x pieces of chocolate in 5 minutes.
Charlotte, taking (x + 3) minutes to eat 1 large piece of chocolate, would eat 5/(x + 3) pieces of chocolate in 5 minutes.
Since they are sharing 2 pieces of chocolate together, the sum of their individual consumption should be equal to 2. Therefore, we can write the following equation:
5/x + 5/x + 5/(x + 3) = 2
Now, we can solve this equation to find the value of x, which represents the time it takes Andy and Ben to eat 1 large piece of chocolate.