finding inequality and solving word prob

Question

temp in R 70 decrease at 2/HR

Temp in s 68 decrease1.5/HR

When will temp in s be higher then in r?

Answer 1

Let x equal the number of hours.

 

The expression for the temperature in Room R is:

70 - 2x

 

The expression for the temperature in Room S is:

68 - 1.5x

 

We want the temperature in Room S > temperature in Room R.

 

Substitute:

68 - 1.5x > 70 - 2x.

 

Solve:

 68 - 1.5x > 70 -2x  (Given)

-68 - 1.5x > 70 - 68 - 2x (Subtract 68 from both sides)

      - 1.5x > 2 - 2x (Simplify)

+2x - 1.5x > 2 - 2x +2x (Add 2x to both sides)

         0.5x > 2 (Simplify)

         2(0.5x) > 2(2) (Multiply both sides by two to isolate x on the left side of the equation... 0.5 is one-half or 1/2, so multiplying by 2 or 2/1 leaves 1x or simply x)

                  x > 4

 

It should take at least four (4) hours.

 

Let's substitute 4 for x in the original equations to check our work.

 

The expression for the temperature in Room R is:
70 - 2x  ==>  70 - 2(4) ==> 70 - 8 ==> 62

The expression for the temperature in Room S is:
68 - 1.5x ==> 68 - 1.5(4) ==> 68 - 6 ==> 62

 

By checking our work, we verify that the room temperatures of Room R and Room S are each 62 degrees after four hours.

 

The temperature in Room S will be higher than the temperature in Room R the instant after four hours have passed.