Two men walk at rates of 6 miles per hour and 10 miles per house, respectively. Simultaneously, they started from the same place walking in opposite directions In how many hours will they be 200 miles apart?
We can start by using the distance formula:
distance = rate x time
Let's call the time it takes for them to be 200 miles apart "t".
During that time, the first man will have walked a distance of 6t, and the second man will have walked a distance of 10t.
Since they are walking in opposite directions, their distances add up to the total distance they are apart:
6t + 10t = 200
Simplifying by combining like terms:
16t = 200
Dividing both sides by 16:
t = 12.5
Therefore, it will take them 12.5 hours to be 200 miles apart.
To find the time it takes for two men to be 200 miles apart while walking in opposite directions at different speeds, we can use the formula:
Time = Distance / Relative Speed
Let's calculate the time it takes for them to be 200 miles apart:
The relative speed of the two men walking in opposite directions is the sum of their individual speeds:
Relative Speed = Speed of Man 1 + Speed of Man 2
Relative Speed = 6 mph + 10 mph
Relative Speed = 16 mph
Now, we can calculate the time:
Time = Distance / Relative Speed
Time = 200 miles / 16 mph
Time = 12.5 hours
Therefore, they will be 200 miles apart in 12.5 hours.