Does a proportional relationship have a constant rate of change?
1 answer:
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Answer:
Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.
Step-by-step explanation:
Two quantities P and Q are said to be in PROPORTION if and only if for all values of P and q, we get:
Here, k : PROPORTIONALITY CONSTANT
Case: 1
5 hour piano practice in 1 week.
So, the piano practice in 2 weeks( 1 x 2) = 2 x 5 = 10 hours
But here, it is given to be 12 hours in 2 weeks.
Hence, NOT PROPORTIONAL.
Case 2:
70 words in 60 seconds.
So, the words typed in 210 seconds ( 60 x 3.5) = 70 x 3.5 = 240 words
But here, it is given to be 280 words in 210 seconds.
Hence, NOT PROPORTIONAL.
Case: 3
8 hour homework in 1 week.
So, the homework done in 2 weeks( 1 x 2) = 2 x 8 = 16 hours
It is given to be 16 hours in 2 weeks.
Hence, PROPORTIONAL.
Case: 4
15 miles in 78 minutes.
So, the distance covered in 102 minutes (78 x 1.3) = 15 x 1.3 = 19.6 miles
But here, it is given to be 17 miles in 102 minutes.
Hence, NOT PROPORTIONAL.
Case: 5
18 miles in 45 minutes.
So, the distance covered in 55 minutes (45 x 1.2) = 18 x 1.2 = 21.6 miles
But here, it is given to be 22 miles in 55 minutes.
Hence, NOT PROPORTIONAL.
Hence, the only proportional case is Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.