Final answer:
To find the time and place of the meeting between the two cars, we need to calculate the time it takes for them to meet. The two cars will meet 1.5 hours after the first car starts its journey at 11:30. The meeting place will be 45 km away from city A.
Step-by-step explanation:
Since the first car leaves at 10:00 and the second car leaves at 10:30, the second car has a head start of 30 minutes, which is equivalent to 0.5 hours. Let's calculate the distance covered by the first car during this time:
Distance = Speed × Time
= 30 km/h × 0.5 h
= 15 km
Now, the remaining distance that the second car needs to cover to meet the first car is:
Remaining Distance = Total Distance - Distance Covered by First Car
= 120 km - 15 km
= 105 km
Since both cars are traveling towards each other, their combined speed is:
Combined Speed = Speed of First Car + Speed of Second Car
= 30 km/h + 40 km/h
= 70 km/h
Using the formula Time = Distance / Speed, we can calculate the time it takes for the two cars to meet:
Time = Remaining Distance / Combined Speed
= 105 km / 70 km/h
= 1.5 hours
Therefore, the two cars will meet 1.5 hours after the first car starts its journey, which is at 11:30.
To find the place of the meeting, we can calculate the distance covered by the first car during this time:
Distance Covered = Speed × Time
= 30 km/h × 1.5 h
= 45 km
The meeting place will be 45 km away from city A, measured from the starting point of the first car.