Question

two cars that are 150 miles apart start driving toward each other on parallel roads. the average speed of the first car is 60 miles per hour. the average speed of the second car is 55 miles per hour. which equation can be used to determine t, the time it takes for the two cars to pass each other?

	rate (mi/h)	time (h)	distance (miles)
first car	60	t	60t
second car	55	t	55t

○ 60t - 55t = 0
○ 60t + 55t = 1
○ 60t + 55t = 150
○ 60t - 55t = 150

Explanation:

Step1: Recall distance formula

Distance = Rate × Time. For each car, distance is calculated as \( 60t \) (first car) and \( 55t \) (second car).

Step2: Analyze total distance

The cars start 150 miles apart and move toward each other. When they pass, the sum of their distances equals the initial separation. So, \( 60t + 55t = 150 \).

Step3: Evaluate options

• Option 1: \( 60t - 55t = 0 \) is for relative speed difference, not total distance.
• Option 2: \( 60t + 55t = 1 \) has wrong total distance (should be 150, not 1).
• Option 3: \( 60t + 55t = 150 \) matches the sum of distances equaling initial separation.
• Option 4: \( 60t - 55t = 150 \) is incorrect as it's a difference, not sum.

Answer:

\( 60t + 55t = 150 \) (the third option)