Question

A town has accumulated 4 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 10 inches, and the depth is increasing by 3 inches every hour. In about how many hours will the snowfall of the towns be equal?

Answer 1

It takes setting up an equation to find when the snow depths are equal, represented by 4 + 6t for Town 1 and 10 + 3t for Town 2. Solving for t, we find that it will take 2 hours for the snowfall to be equal in both towns.

Step-by-step explanation:

The question involves calculating the time it will take for the snowfall in two towns to be equal given their respective starting snow depths and rates of increase in snow depth. To solve this, we can set up an equation where we equate the snow depths of the two towns as they increase over time.

Let t be the number of hours it takes for the snow depths to be equal. The first town has 4 inches of snow and is accumulating at a rate of 6 inches per hour, so its snow depth can be represented as 4 + 6t. The second town starts with 10 inches of snow and is accumulating at 3 inches per hour, so its depth is 10 + 3t.

We want to find t when the snow depths are equal, so we set the expressions equal to each other:

4 + 6t = 10 + 3t

Solve for t:

Subtract 3t from both sides: 4 + 6t - 3t = 10 + 3t - 3t which simplifies to 4 + 3t = 10.

Then subtract 4 from both sides: 3t = 10 - 4 which simplifies to 3t = 6.

Finally, divide both sides by 3: t = 6 / 3, which simplifies to t = 2.

Therefore, it will take 2 hours for the snowfall in both towns to be equal.

Answer 2

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Answer:

2 hours

Step-by-step explanation:

The initial difference in depth is 10-4 = 6 inches. The difference in snowfall rates is 6-3 = 3 inches per hour.

At that rate, the difference in depth will be made up in ...

(6 in)/(3 in/h) = 2 h

In 2 hours the snowfall in the two towns will be equal.

_____

You could write equations for depth, then equate them.

d1 = 4 +6h

d2 = 10 +3h

d1 = d2 . . . . . . . . . . for some value of h the depths will be equal

4 +6h = 10 +3h

h(6 -3) = 10 -4 . . . . . subtract 3h+4 from both sides

h = 6/3 = 2

Snowfall will be equal in 2 hours.