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?

Answer 1

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.