Question

Two towns 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 hour. In how many hours will the snowfalls of the towns be equal?

Answer 1

Let umber of hours in which snowfalls of the both towns become  equal = x

Given that rate at which snow depth is increasing in town 1 =

$3\ \frac{1}{2}=\frac{2*3+1}{2}=\frac{6+1}{2}=\frac{7}{2}$ inches per hour

Then amount of snow fall in x hours in twon 1 = $\frac{7}{2}x$

Given that rate at which snow depth is increasing in town 2 =

$2\ \frac{1}{4}=\frac{2*4+1}{4}=\frac{8+1}{4}=\frac{9}{4}$ inches per hour

Then amount of snow fall in x hours in twon 2 = $\frac{9}{4}x$

when snow fall becomes equal then we get equation:

$\frac{9}{4}x = \frac{7}{2}x$

$\frac{9}{4}x = \frac{14}{4}x$

$0 = \frac{14}{4}x-\frac{9}{4}x$

$0 = \frac{5}{4}x$

$0*\frac{4}{5}=x$

0=x

Hence final answer is 0 hours.

Answer 2

Answer:

$t = 0.8(x_2 - x_1)$

Step-by-step explanation:

In order to answer this question we have to make the following assumptions:

Let $x_1, x_2$ be the amount of snow already present in town 1 and town 2 respectively.

It is given that the snow is increasing at a rate of:

Town 1:  $3\frac{1}{2}$ inches per hour

Town 2: $2\frac{1}{4}$ inches every hour

We have to find the after how many hours the snowfall in towns be equal. Let t be the number of hours after which the two towns have equal amount of snow.

Town 1: $x_1 + 3\displaystyle\frac{1}{2}t$

Town 2: $x_2 + 2\displaystyle\frac{1}{4}t$

Equating the two equation:

$x_1 + 3\displaystyle\frac{1}{2}t = x_2 + 2\displaystyle\frac{1}{4}t\\\\\frac{7}{2}t - \frac{9}{4}t = x_2 - x_1\\\\\frac{5}{4}t = x_2 - x_1\\\\ t = 0.8(x_2 - x_1)$

Thus, for different values of $x_1, x_2$, we have different values for time for which the two towns will have equal amount of snow.