Question

in the city of syracuse, 6 meters of snow fall in 30 days. at this rate, how much time would it take for 24 meters of snow to fall?
(a) let ( t ) be the unknown amount of time it would take (in days). using the values below, create a proportion that can be used to find ( t ).
values: ( t ), ( 6 ), ( 30 ), ( 24 )
( \frac{square}{square} = \frac{square}{square} )
(b) use the proportion from part (a) to find the time it would take for 24 meters of snow to fall. do not round any computations.
( square ) days

Explanation:

Step1: Set up proportional relationship

We relate snowfall to time consistently.
$\frac{6}{30} = \frac{24}{t}$
(Alternative valid proportion: $\frac{30}{6} = \frac{t}{24}$ also works, the above pairs snowfall over time for both cases)

Step2: Cross-multiply to solve for $t$

Cross multiply to isolate the unknown.
$6 \times t = 24 \times 30$

Step3: Calculate right-hand side

Compute the product on the right.
$6t = 720$

Step4: Solve for $t$

Divide both sides by 6.
$t = \frac{720}{6} = 120$

Answer:

(a) $\boldsymbol{\frac{6}{30} = \frac{24}{t}}$ (or equivalent like $\frac{30}{6} = \frac{t}{24}$)
(b) $\boldsymbol{120}$ days