Towns math

Question

Two towns have accumulated different amounts of snow in town 1 the snow depth is increasing by 3 1/2 inches every hour in town 2 the snow depth is increasing by 2 1/4 inches every house in how many hours will the snowfalls of the towns be equal

Answer 1

So then let T1 be the amount of snow town #1 has and T2 be the amount of snow town#2 has.
Given the missing data, we are forced to assume that Town #1 has less snow than Town #2 as
the snowfall rate is faster. Otherwise, like Mark said, there is no way Town #2 can catch up.
Hence, we have T1 < T2.

So the two linear equation models are : Town #1: 3.5X + T1
Town #2: 2.25X + T2
where X is the time in hours.

Setting these two equations equal and solving for X:
3.5X + T1 = 2.25X + T2
1.25X + T1 - T2 = 0

1.25X = (T2-T1)
X = (T2-T1)/1.25 = 0.8(T2-T1) <-- note here the reciprocal of 1.25 = 1/1.25 = the reciprocal of 5/4 = 4/5=0.8

So when you get the original numbers, just plug them into the equation above to find the answer.

For example, suppose Town #1 has 5 inches of snow and Town #2 has 10 inches of snow.
You then plug T1=5 and T2=10 into the equation I derived for you.
So X = 0.8(T2-T1) = 0.8(10-5) = 0.8*5 = 4

so after four hours they both have 19 inches of snow:
Town #1: 5 + 4(3.5) = 5 + 14 = 19
Town #2: 10 + 4(2.25) = 10 + 9 = 19

Am originally from Youngstown, Ohio.
Greetings fellow Buckeye.
I HATE SNOW!!!!
I don't miss it!!!
I never want to see it again. EVER. PERIOD