Question

Gretchen lives in Florida, for the current temperature 69°F and rising at a rate of 2°F per hour. She's talking on the phone to her friend in Indiana where the temperature is now 84°F and falling at a rate of 3°F per hour.

A.) If the temperature continue changing at the same rates, how many hours would Gretchen and her friend have to talk before the temperature become equal?
B.) What will the temperature be?

Answer 1

69 + 2h = 84 - 3h
2h + 3h = 84 - 69
5h = 15
h = 15/5
h = 3 <=== the temps will be the same in 3 hrs

69 + 2(3) = 69 + 6 = 75
84 - 3(3) = 84 - 9 = 75

and the temps will both be 75 F <==

Answer 2

A) Gretchen and her friend have to talk 3 hours before the temperature become equal.

B) The temperature after 3 hours will be 75°F.

Explanation:

Current temperature in Florida = 69°F

Rate at which temperature is rising = 2°F per hour

Current temperature in Indiana = 84°F

Rate at which temperature is falling= 3°F per hour

A) Suppose in x hours both places have same temperature:

`69^oF +2F^o* x=84^oF-3^oF* x`

`5x=84^oF-69^oF`

x = 3 hours

Gretchen and her friend have to talk 3 hours before the temperature become equal.

B) The temperature after 3 hours:

x = 75°F

`69^oF +2F^o* x=69^oF +2F^o* 3=75^oF`