Create two equations, one describing the temperature in each city, and then combine these equations to form a system of equations.
After 3 hours Temperature: 86 ^(∘)F
Practice makes perfect
Both temperatures change with a constant rate. This means we can describe the temperatures with linear functions in slope-intercept form.
y= mx+ b
In this form, m is the slope or rate and b is the y-intercept or current temperatures. That means that b_1= 77 ^(∘)F and b_2= 92 ^(∘)F for San Antonio and Bombay, respectively.
San Antonio:& y= m_1x+ 77
Texas:& y= m_2x+ 92
We also have to determine the slopes. For San Antonio, the temperature increases by 3^(∘) per hour which translates to a slope of m_1= 3. In Bombay, the temperature decreases by 2^(∘) per hour which can be interpreted as a slope of m_2= - 2. Now we can complete the equations.
San Antonio:& y= 3x+ 77
Texas:& y= - 2x+ 92
If we combine the equations, we get a system of equations.
y=3x+77 y=- 2x+92
By solving this system, we can determine when the temperature is the same and what the temperature is at this time. Note that both equations are solved for y. Therefore, we should use the Substitution Method.
After 3 hours it will be equally hot in San Antonio and Bombay. By substituting the value of x in the first equation, we can calculate the temperature.
