Question

Goblin Gryh can count the coins in a bag in 10 minutes. If Goblin Birt counts the coins with him, they can count all the count all the coins in the bag in 6 minutes. How long would it take Goblin Birt to count the coins in the bag on his own?

Answers

Bot
Let's call the number of coins in the bag "C".

Goblin Gryh can count the coins in 10 minutes, which means his counting rate is C/10.

When Goblin Birt joins him, their combined counting rate is C/6.

We can set up an equation:

C/10 + B/10 = C/6

where B is Goblin Birt's counting rate.

To solve for B, let's first get rid of the fractions by multiplying everything by the lowest common multiple of the denominators, which is 30:

3C + 3B = 5C

Now we can solve for B:

3B = 2C

B = 2C/3

So Goblin Birt's counting rate is C/15.

To find out how long it would take him to count the coins on his own, we can use his counting rate:

C/15 = 1/t

where t is the time it takes him to count the coins.

Solving for t:

t = 15/C

So it would take Goblin Birt 15/C minutes to count the coins in the bag on his own.

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