Ben and Ken live in homes that are 10 miles apart. Both left their respective home at 10:00 am to visit the other person. If Ben travels at an average speed of 35mph and Ken 45 mph, at what time will they cross each other?
To find out when Ben and Ken will cross each other, we can determine the time it takes for both of them to cover the distance between their homes.
Let's calculate the time for Ben first:
Distance = Speed * Time
Since Ben travels at an average speed of 35 mph and the distance is 10 miles, we can write:
10 miles = 35 mph * Ben's time
Dividing both sides of the equation by 35 mph, we get:
Ben's time = 10 miles / 35 mph
Calculating this, we find:
Ben's time = 0.2857 hours
Now let's calculate the time for Ken:
Distance = Speed * Time
Since Ken travels at an average speed of 45 mph and the distance is 10 miles, we can write:
10 miles = 45 mph * Ken's time
Dividing both sides of the equation by 45 mph, we get:
Ken's time = 10 miles / 45 mph
Calculating this, we find:
Ken's time = 0.2222 hours
Now, let's determine the time it takes for both of them to cross each other. It will be the maximum value of Ben's time and Ken's time.
Max time = Max(Ben's time, Ken's time) = Max(0.2857, 0.2222) hours
Calculating the maximum value, we find:
Max time = 0.2857 hours
Since they left their respective homes at 10:00 am, we can add the maximum time to this starting time to determine when they will cross each other.
Crossing time = 10:00 am + Max time
Adding the time, we get:
Crossing time = 10:00 am + 0.2857 hours
Converting 0.2857 hours to minutes, we find:
Crossing time = 10:00 am + 17.1428 minutes
Adding the minutes, we get:
Crossing time = 10:17 am (rounded to the nearest minute)
Therefore, Ben and Ken will cross each other at approximately 10:17 am.
To determine at what time Ben and Ken will cross each other, we need to find out how long it will take each person to travel their respective distances.
First, let's calculate how long it will take Ben to travel 10 miles at a speed of 35 mph. We can use the formula: time = distance / speed.
For Ben:
Time taken = 10 miles / 35 mph = 0.2857 hours (rounded to four decimal places)
Now, let's calculate how long it will take Ken to travel 10 miles at a speed of 45 mph.
For Ken:
Time taken = 10 miles / 45 mph = 0.2222 hours (rounded to four decimal places)
Since they both started at the same time, we need to find out when their travel times add up to determine the time when they will cross each other.
Total time for Ben and Ken to cross each other = 0.2857 hours + 0.2222 hours = 0.5079 hours (rounded to four decimal places)
Now, let's convert the total time from hours to minutes. Since there are 60 minutes in one hour, we multiply the total time by 60.
Total time in minutes = 0.5079 hours * 60 minutes/hour = 30.474 minutes (rounded to three decimal places)
To determine the crossing time, we'll add the total time to the initial starting time of 10:00 am.
Crossing time = 10:00 am + 30.474 minutes = 10:30:28 am (rounded to the nearest second)
Therefore, Ben and Ken will cross each other at approximately 10:30:28 am.