We have been given that a town has accumulated 3 inches of snow and the Snow depth is increasing by 5 inches every hour. Further we are given that a nearby town has accumulated 10 inches and the depth is increasing by 2 inches every hour.
Let us assume that after x hours the snowfall of both the towns will be equal.
We can express snowfall of first town after x hours as [tex]3+5x[/tex] and we can express the snowfall of of the second town after x hours as [tex]10+2x[/tex].
In order to find the time when snowfalls of the two towns will be equal, we set up:
[tex]3+5x=10+2x[/tex]
[tex]5x-2x=10-3[/tex]
[tex]3x=7[/tex]
[tex]x=\frac{7}{3}\text{ hours}[/tex]
Therefore, snowfall of the two towns will be equal after [tex]\frac{7}{3}\text{ hours}[/tex]
