Question

a truck enters a highway driving 60 mph. a car enters the highway at the same place 12 minutes later and drives 70 mph in the same direction. from the time the car enters the highway, how long will it take the car to pass the truck? the car will pass the truck in \\(\square\\) minutes. (round to the nearest minute.)

Explanation:

Step1: Convert 12 mins to hours

$12\ \text{minutes} = \frac{12}{60} = 0.2\ \text{hours}$

Step2: Calculate truck's head start distance

Distance = speed × time: $d = 60 \times 0.2 = 12\ \text{miles}$

Step3: Set up relative speed equation

Let $t$ = time (hours) for car to catch up. Relative speed = $70 - 60 = 10\ \text{mph}$. The car must cover 12 miles at this relative speed:
$10t = 12$

Step4: Solve for $t$ in hours

$t = \frac{12}{10} = 1.2\ \text{hours}$

Step5: Convert $t$ to minutes

$1.2 \times 60 = 72\ \text{minutes}$

Answer:

72