Question

The temperature in Syracuse NY started at -14C and rose 2 degrees every hour. The temperature in mamaroneck, NY started at -2C and rose 1 degree every 2 hours. Write a system of equations modeling the temperature for each city.

Answer 1

`\begin{gathered} S=-14+2h \\ M=-2+(h)/(2) \end{gathered}`

Step-by-step explanation

Let the temperature in Syracuse be S.

Let the temperature in Mamaroneck be M.

Let the number of hours be h.

The starting temperature in Syracuse was -14°C and rose 2 degrees every hour. This implies that the temperature at any given hour is the sum of the starting temperature and the product of the number of hours and 2.

That is:

`S=-14+2h`

where h = number of hours

The starting temperature in Mamanoreck was -2°C and rose 1 degree every 2 hours. Since it rose 1 degree every 2 hours, it implies that in 1 hour, the temperature rise is:

`\begin{gathered} 2hr=1\degree C \\ 1hr=(1)/(2)\degree C \end{gathered}`

This implies that the equation modeling the temperature in Mamanoreck is:

`M=-2+(h)/(2)`