Write and solve an equation to find date in the month when the temperature in Hearthtown and Polk were the same

Question

The temperature on January 1 in Hearthtown was 88 F. The temperature decreased by 2 F each day. The temperature in Polk on January 4 was 52 F. The temperature increased by 4 F each day.

Answer 1

Let n = number of day

Let t = temperature

 

HEARTHTOWN:

 

     On Jan 1, temp is 88°. ... on Jan 4 (3 days later), it is 82° ...88 - 2(3) = 82° ...  it drops 2° per day 

     

     So, this equation represents the temperature, n days after Jan 4th

 

     t = 82 - 2n  ... starting temperature is 82°, and it falls 2° per day

     

 

POLK:

 

     On Jan 4, temp is 52.  It rises 4° per day

 

     t =  52 + 4n

 

The temperatures will be the same a single value of n produces the same temperature for both equations

 

     52 + 4n = 82 - 2n

     4n + 2n = 82 - 52

     6n = 30

       n = 5

 

The temperatures will be the same 5 days after  Jan. 4th.

The temperatures will be 72° on January 9th