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?
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.
Let's assume that Goblin Gryh counts at a rate of 'G' coins per minute and Goblin Birt counts at a rate of 'B' coins per minute.
We are given two pieces of information:
1) Goblin Gryh can count the coins in a bag in 10 minutes, so his rate is G = 1/10 coins per minute (since 1 bag in 10 minutes).
2) If Goblin Birt counts the coins with Goblin Gryh, they can count all the coins in the bag in 6 minutes, so their combined rate is G + B = 1/6 coins per minute (since 1 bag in 6 minutes).
To find out how long it would take Goblin Birt to count the coins in the bag on his own, we need to determine B.
From the second piece of information, we can subtract G from both sides of the equation to get:
B = 1/6 - 1/10
B = (10 - 6) / (10 * 6)
B = 4 / 60
B = 1/15 coins per minute (since 1 bag in 15 minutes)
Therefore, Goblin Birt can count the coins in the bag on his own at a rate of 1/15 coins per minute.
To calculate the time it would take Goblin Birt to count the coins in the bag on his own, we can set up the equation:
1 bag = (1/15) coins/minute * T minutes,
where T represents the time in minutes taken by Goblin Birt.
Simplifying the equation, we have:
1 = (1/15) * T
To solve for T, we multiply both sides of the equation by 15:
15 = T
Therefore, it would take Goblin Birt 15 minutes to count the coins in the bag on his own.