On a winter evening at sundown, a Kansas City news station reports that the temperature is −2∘F and will drop by 2∘F per hour until sunrise. At the same time, a Chicago news station reports that the temperature is 6∘F and will drop by 4∘F per hour.Which equation can you use to find h, the number of hours it will take the cities to reach the same temperature?Choices:(A) −2−2h=6−4h(B) 2h−2=6h−4How long will it take for the cities to reach the same temperature?Simplify any fractions.____ hours
Q. On a winter evening at sundown, a Kansas City news station reports that the temperature is −2∘F and will drop by 2∘F per hour until sunrise. At the same time, a Chicago news station reports that the temperature is 6∘F and will drop by 4∘F per hour.Which equation can you use to find h, the number of hours it will take the cities to reach the same temperature?Choices:(A) −2−2h=6−4h(B) 2h−2=6h−4How long will it take for the cities to reach the same temperature?Simplify any fractions.____ hours
Set up Kansas City equation: Let's set up the equation for Kansas City first. The temperature starts at −2°F and drops by 2°F each hour. So, after h hours, the temperature in Kansas City will be −2−2h.
Set up Chicago equation: Now let's set up the equation for Chicago. The temperature starts at 6°F and drops by 4°F each hour. So, after h hours, the temperature in Chicago will be 6−4h.
Set temperatures equal: To find when the temperatures will be the same, we set the two expressions equal to each other. This gives us the equation −2−2h=6−4h.
Add 4h to both sides: Now we need to solve for h. First, let's add 4h to both sides to get the h terms on one side.−2−2h+4h=6−4h+4hThis simplifies to −2+2h=6.
Isolate term with h: Next, we add 2 to both sides to isolate the term with h.−2+2+2h=6+2This simplifies to 2h=8.
Solve for h: Finally, we divide both sides by 2 to solve for h. 22h=28This gives us h=4.
More problems from Solve linear equations with variables on both sides: word problems