A scarf is knitted at a rate of 3/7 inch per half hour. How much length is added to the scarf in a 6 hour period?
This needs a set up for a 3rd grader just starting with fractions. I showed her this:
3/7 inch in a half hour, so 6/7 of an inch in an hour. So, 6/7 x 6 = 36/7 inches added
(Kate's teacher said that her answer of '18/7 hours' was correct. Help!?!
You are correct at 36/7
another way to look at it:
there are 12 half-hours in 6 hours. Have Katie look at a clock.
So the length is 12*(6/7) = 36/7 inches
To solve this problem, we need to break it down into smaller steps that are easier to understand. Let's start by understanding the given information.
We know that a scarf is being knitted at a rate of 3/7 inch per half hour. This means that in every half hour, the length of the scarf increases by 3/7 of an inch.
To find out how much length is added to the scarf in a 6-hour period, we need to multiply the rate of increase by the number of half hours in 6 hours. Let's break it down step by step:
1. Identify the rate of increase per hour:
Since we know that 3/7 inch is added in a half hour, we need to determine the rate of increase per hour.
To do this, we can double the rate of increase per half hour to get the rate of increase per hour.
3/7 inch per half hour x 2 = 6/7 inch per hour.
2. Determine the number of half hours in 6 hours:
Since there are 6 half hours in 6 hours (each hour consists of two half hours), we need to multiply the rate of increase per hour by the number of half hours in 6 hours.
6/7 inch per hour x 6 half hours = 36/7 inch added in 6 hours.
So, in a 6-hour period, 36/7 inch of length is added to the scarf.
Now, let's address the explanation discrepancy. The teacher's answer of '18/7 hours' seems incorrect. The question asks for the amount of length added, not the time taken to add that length. Therefore, the answer should be given in inches, not hours.