Clayton wants to be a musician. After school one afternoon, he spends 1 over 2 of his time practising the drums and 3 over 4 of the remaining time working on homework and eating dinner. He spends the remaining 3 over 4 h texting and talking to his friends. How long did he practise the drums?
Let's assume Clayton has t hours after school.
He spends 1/2 * t hours practicing the drums.
The remaining time is t - 1/2 * t = 1/2 * t.
He spends 3/4 * (1/2 * t) hours working on homework and eating dinner.
So, he spends 3/4 * (1/2 * t) = 3/8 * t hours working on homework and eating dinner.
The remaining time is 1/2 * t - 3/8 * t = 4/8 * t - 3/8 * t = 1/8 * t.
Therefore, Clayton spends 1/8 * t = 3/4 hours texting and talking to his friends.
As 1/8 * t is equal to 3/4 hours, we can set up the equation 1/8 * t = 3/4.
Multiplying both sides of the equation by 8 gives us t = 6.
Therefore, Clayton has 6 hours after school.
So, he spends 1/2 * 6 = 3 hours practicing the drums. Answer: \boxed{3}.
To find out how long Clayton practiced the drums, let's follow the given information step-by-step:
Step 1: Find out how much time Clayton spent on homework and eating dinner:
He spent 3/4 of the remaining time on homework and eating dinner.
Step 2: Find out how much time Clayton spent texting and talking to friends:
He spent the remaining 3/4 hours texting and talking to friends.
Step 3: Calculate the total remaining time:
The total time remaining is the sum of the time spent on homework and eating dinner and the time spent texting and talking to friends.
Step 4: Subtract the total time remaining from the time Clayton has after school:
The remaining time after school is 1/2.
Step 5: Subtract the total remaining time from the time Clayton has after school to find how much time he spent practicing the drums.
Let's calculate it step-by-step:
Step 1:
3/4 of the remaining time on homework and eating dinner
= (3/4) * 1/2
= 3/8
Step 2:
The remaining time spent texting and talking to friends:
= 3/4
Step 3:
The total remaining time:
= (3/4) + (3/8)
= 6/8 + 3/8
= 9/8
Step 4:
The remaining time after school is 1/2.
Step 5:
Time spent practicing the drums:
= Remaining time after school - Total remaining time
= 1/2 - 9/8
To subtract fractions, we need to make the denominators the same:
= (1/2) - (9/8)
= (4/8) - (9/8)
= -5/8
The time spent practicing is -5/8 hours. However, since time cannot be negative, we can conclude that Clayton did not spend any time practicing the drums in this scenario.
To find out how long Clayton practiced the drums, let's break down the given information step by step.
Let's assume that Clayton has a total of 4 units of time after school (which can represent hours or any other time unit).
1. Clayton spends 1/2 of his time practicing the drums. This means he spends (1/2) x 4 = 2 units of time practicing.
2. After practicing the drums, Clayton has the remaining time. Since he started with 4 units and spent 2 units on practicing, he has 4 - 2 = 2 units of time left.
3. Clayton then spends 3/4 of the remaining time on homework and eating dinner. This is (3/4) x 2 = 6/4 = 1.5 units of time.
4. After finishing homework and dinner, Clayton has the remaining time. Since he spent 1.5 units on homework and dinner, he has 2 - 1.5 = 0.5 units of time left.
5. Finally, Clayton spends 3/4 of the remaining time on texting and talking to his friends. This is (3/4) x 0.5 = 3/8 = 0.375 units of time.
Since Clayton has 0.5 units of time left, which is equal to 0.375 units of time spent on texting and talking to friends, we can deduce that the remaining amount of time is spent on practicing the drums.
Therefore, Clayton spent 0.5 units of time, or 0.5 hours, practicing the drums.