Ted practices two types of swimming styles for a total of 50 minutes everyday. He spends 20 minutes more practicing the breast stroke than the butterfly stroke. Part A: write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stoke everyday (X) and the number of minutes he practices the breast stroke everyday (Y) Part B:How much time does Ted spend on practicing the breast stroke every day? Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke everyday ? Explain your reasoning

Question

Ted practices two types of  swimming styles  for a total of 50 minutes everyday. He spends 20 minutes more practicing  the breast stroke than the butterfly stroke. Part A: write a pair of linear equations to show  the relationship between the number of minutes Ted practices  the butterfly stoke everyday (X) and the number  of minutes he practices the breast stroke everyday (Y) Part B:How much time does Ted spend on practicing  the breast stroke every day? Part C: Is it possible  for Ted to have spent 45 minutes practicing the butterfly stroke everyday ? Explain your reasoning

anonymous · Answer

To start with we have:

X = minutes of butterfly and Y = minutes of breaststroke.

We are told that the total time = 50minutes. We are also told that however many minutes of butterfly Ted does, he does 20minutes more than that of breaststroke. 

PART A:
Using the first piece of information we know that:
$$X+Y=50$$

Using the second piece of information can represent the total amount of breaststroke time with the following equation:
$$Y = X +20$$

So our linear equations are:
$$X+Y=50$$$$Y = X +20$$

PART B
We can clean up our answers from PART A a little bit and make it easier to work with if we solve the first equation for Y. If we do that we get:
$$Y=50-X$$$$Y = X +20$$

Common scene tells us that Y=Y. So:
$$Y=Y$$$$50-X=X+20$$$$2X=30$$$$X=15 minutes$$
Ted practices the butterfly stroke for 15 minutes every day.

We also know that the total time is 50 minutes. If he spends 15minutes on butterfly, simple subtraction tells us that he must spend 35minutes on breaststroke. 

We can check both of these answers but plugging values into out original two equations:
$$X+Y=50$$$$15+25=50$$

and 
$$Y = X +20$$$$35 = 15 +20$$

PART C:
We know that for however much time Ted spends on the butterfly he spends 20minutes more on breaststroke. If he spends 45minutes on butterfly then he must spend 45+20=65minutes on breaststroke. BUT, we already know that he only spends 50minutes total.  So:

No, it is not possible for Ted to spend 45minutes on butterfly everyday.

anonymous · Answer

thanks