Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. (5 points)

Part B: How much time does Melvin spend swimming every day? Show your work. (3 points)

Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning. (2 points)

A)   x + y = 110

      x - y = 40

B) Melvin swims for 35 minutes every day.

C) It is not possible

Step-by-step explanation:

Step 1:

Let x denote the duration for which Melvin plays tennis and y denote the duration for which he swims

Step 2 :

Part A :

Given that the total duration for which he plays and tennis is 110 minutes

so we have x + y = 110

Also given that he plays tennis for 40 minutes more than he swims

So, x = y+ 40 =>x-y = 40

So the linear pair of equations are

x + y = 110

x-y = 40

Step 3 :

Part B

Solving the above 2 equations we have

y+40+y = 110 = > 2y+ 40 = 110 = > y = 2y = 70 = >35

x = y+40 = 35+ 40 = 75

So Melvin plays tennis for 75 minutes and swims for 35 minutes every day.

Step 4 :

Part C

Given he plays and swims for 110 mins exactly, i.e x + y = 110

If Melvin plays tennis for 70 minutes , then x = 70,  then the time for which he can swim is 110 - 70 = 40 mins.

He gets only 40 mins for swimming which is not 40 mins more than he plays tennis .

So this case is not possible.

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