Anthony leaves kingstons at 2:00 pm and drives to queensville, 160mi distant, at 45 mph. At 2:15 pm Helen leaves queensville and drives to kingston at 40mph. At what time do they pass each other on the road?
If we place Kingston at (0,0) and Queensville at (0,160), then a time t from when Anthony left, the positions will be equal:
45t = 160-40(t - 1/4)
t = 2
So, they meet at 2:00+2 = 4:00 pm
Or, consider it like this. In the first 15 minutes, Anthony went 45/4 miles. The two cars are approaching each other at 85 mi/hr, so how long does it take to cover the remaining distance?
(160-45/4)/85 = 7/4
That is, they meet 7/4 hours after Helen started.
To find the time at which Anthony and Helen pass each other on the road, we need to determine how long it takes them to meet.
Let's start by calculating the travel time for Anthony. He drives a distance of 160 miles at a speed of 45 mph. Using the formula:
Time = Distance / Speed
we can calculate Anthony's travel time:
Time = 160 miles / 45 mph = 3.56 hours
Since Anthony leaves at 2:00 pm, we can add 3.56 hours to find the time when he reaches the meeting point:
2:00 pm + 3.56 hours = 5:33 pm (approx.)
Now, let's calculate Helen's travel time. She leaves Queensville at 2:15 pm and drives to meet Anthony in Kingston, which is 160 miles away. Since Anthony started at 2:00 pm, there is a 15-minute difference between their departure times. We need to adjust for this difference by subtracting 15 minutes from Helen's travel time.
15 minutes = 0.25 hours
So, Helen's travel time is:
Time = 160 miles / 40 mph = 4 hours - 0.25 hours = 3.75 hours
Now, we add 3.75 hours to Helen's departure time of 2:15 pm to find the time when she reaches the meeting point:
2:15 pm + 3.75 hours = 6:00 pm (approx.)
Therefore, Anthony and Helen will pass each other on the road at approximately 6:00 pm.
To determine when Anthony and Helen pass each other on the road, we can calculate the time it takes for each of them to reach the meeting point.
First, let's calculate the time it takes for Anthony to travel 160 miles at a speed of 45 mph:
Time taken by Anthony = Distance / Speed
Time taken by Anthony = 160 miles / 45 mph = 3.56 hours (rounded to two decimal places)
Next, let's calculate the time it takes for Helen to travel from Queensville to the meeting point, which is the same distance as Anthony has traveled:
Time taken by Helen = Distance / Speed = 160 miles / 40 mph = 4 hours
Since Helen left 15 minutes (0.25 hours) after Anthony, we need to adjust her time:
Adjusted time taken by Helen = Time taken by Helen - Delay
Adjusted time taken by Helen = 4 hours - 0.25 hours = 3.75 hours (rounded to two decimal places)
Now, we can determine the total time it takes for both of them to meet:
Total time = Time taken by Anthony + Adjusted time taken by Helen
Total time = 3.56 hours + 3.75 hours = 7.31 hours (rounded to two decimal places)
Therefore, they pass each other on the road approximately 7 hours and 19 minutes (0.31 hours) after Anthony leaves. Adding this time to the initial departure time:
Passing time = 2:00 pm + 7 hours and 19 minutes
Passing time = 9:19 pm
So, they will pass each other on the road around 9:19 pm.