Two Cars

A car leaves San Francisco, traveling east at 65 miles per hour.
The driver takes a bathroom break of 15 min every 3 hours.
Another car departs New York City at the same time, traveling at 60 miles per hour.
This driver takes a bathroom break of only 10 minutes every 4 hours.
Assuming they both sleep 6 hours a day (from 12 midnight to 6 am each day),

(Cars travel the same roads, traffic can be ignored and acceleration is assumed to be instantaneous?)

When they meet?

To solve this problem, you need to know the total distance by road from NYC to San Francisco.

The total distance by road from New York City to San Francisco is approximately 2,900 miles.

Since both cars are traveling continuously except for bathroom breaks and sleep, we can determine when they will meet by calculating the time each car takes to travel the distance.

Car 1:
Speed = 65 mph
Time to travel 2,900 miles = Distance / Speed
Time to travel 2,900 miles = 2,900 miles / 65 mph
Time to travel 2,900 miles = 44.62 hours

Car 2:
Speed = 60 mph
Time to travel 2,900 miles = Distance / Speed
Time to travel 2,900 miles = 2,900 miles / 60 mph
Time to travel 2,900 miles = 48.33 hours

Now, let's calculate the time spent on bathroom breaks and sleep:

Car 1's bathroom breaks:
Bathroom break duration = 15 minutes
Number of bathroom breaks = Total travel time / Bathroom break interval
Number of bathroom breaks = 44.62 hours / 3 hours
Number of bathroom breaks = 14.87 breaks

Car 2's bathroom breaks:
Bathroom break duration = 10 minutes
Number of bathroom breaks = Total travel time / Bathroom break interval
Number of bathroom breaks = 48.33 hours / 4 hours
Number of bathroom breaks = 12.08 breaks

Both cars sleep for 6 hours a day. Considering they sleep between 12 midnight to 6 am, the total sleep duration during their travel time would be:

Total sleep duration = 6 hours/day x (number of days - 1)
Total sleep duration = 6 hours x (44.62 hours / 24 hours)
Total sleep duration = 11.08 hours

Now let's calculate the actual travel time for both cars:

Car 1's total travel time = Total time - Bathroom breaks - Sleep duration
Car 1's total travel time = 44.62 hours - (14.87 breaks x 15 minutes) - 11.08 hours
Car 1's total travel time = 44.62 hours - 3.72 hours - 11.08 hours
Car 1's total travel time = 29.82 hours

Car 2's total travel time = Total time - Bathroom breaks - Sleep duration
Car 2's total travel time = 48.33 hours - (12.08 breaks x 10 minutes) - 11.08 hours
Car 2's total travel time = 48.33 hours - 2.01 hours - 11.08 hours
Car 2's total travel time = 35.24 hours

Since both cars start at the same time, their meeting point can be determined by comparing their travel times. The car with the lesser travel time will reach the meeting point first.

Therefore, Car 2 will reach the meeting point first since Car 2's total travel time (35.24 hours) is less than Car 1's total travel time (29.82 hours).

To calculate the actual time when they meet, you can divide their travel time into intervals and determine the exact time.

To find the total distance by road from New York City to San Francisco, you can use any route planning tool or map service like Google Maps.

Once you have the total distance, you can calculate the time it takes for each car to reach the meeting point, considering the speed and breaks taken by the drivers.

Let's break down the solution step by step:

1. Find the total distance by road from New York City to San Francisco using a map or route planning tool. Let's say the total distance is D miles.

2. The first car is traveling at a speed of 65 miles per hour and takes a 15-minute break every 3 hours. So, for every 3 hours of driving, the car effectively covers 65 * 3 miles.

3. The second car is traveling at a speed of 60 miles per hour and takes a 10-minute break every 4 hours. So, for every 4 hours of driving, the car effectively covers 60 * 4 miles.

4. Both drivers sleep for 6 hours a day, from 12 midnight to 6 am. Therefore, they do not drive during this time.

5. Let's assume the cars start at the same time at 12 noon.

6. The total driving time for each car can be calculated by subtracting the time spent on breaks and sleep from the total time from 12 noon to 12 midnight (12 hours).

a. The first car drives for 12 hours, but takes 15-minute breaks every 3 hours and sleeps for 6 hours. So, the total driving time for the first car is 12 - (6/60) - (15/60) - (15/60) - (15/60) hours.

b. The second car drives for 12 hours, takes 10-minute breaks every 4 hours, and sleeps for 6 hours. So, the total driving time for the second car is 12 - (6/60) - (10/60) - (10/60) - (10/60) hours.

7. Now, you can calculate the distance covered by each car during their respective driving times:

a. The distance covered by the first car = (Total driving time for the first car) * (Speed of the first car).

b. The distance covered by the second car = (Total driving time for the second car) * (Speed of the second car).

8. The meeting point is reached when the distance covered by both cars sums up to the total distance between New York City and San Francisco.

Total distance = Distance covered by the first car + Distance covered by the second car.

9. Solve for the meeting point using the equations from step 8.

By following these steps, you can find when the two cars meet on their journey from New York City to San Francisco.