Tina and Jim live 5 miles apart from each other. Tina ran from her house to Jim's house at a rate of 10 miles per hour. Jim ran from his house to Tina's house at a rate of 8 miles per hour. How far had Jim run by the time he crossed paths with Tina?
they are approaching at the rate of 18 mi/hr
They only had to cover 5 miles, so that took 5/18 hours
In that time, Jim ran 10 * 5/18 = 25/9 miles
To find out how far Jim had run when he crossed paths with Tina, we need to determine when that happened first.
Let's assume t represents the time it took for Jim to cross paths with Tina.
Since Tina ran at a rate of 10 miles per hour and the distance between their houses is 5 miles, she would have traveled a total distance of 10 * t miles.
Jim, on the other hand, ran at a rate of 8 miles per hour and would have traveled a total distance of 8 * t miles.
Since they met at a point equidistant from their houses, the total distance Tina traveled must be equal to the total distance Jim traveled.
Therefore, we can set up the equation: 10 * t = 8 * t
Simplifying the equation, we get: 2 * t = 5
Dividing both sides by 2, we find that t = 2.5.
So, it took Jim 2.5 hours to cross paths with Tina.
To determine how far Jim had run by that point, we can substitute the value of t into the equation 8 * t:
8 * 2.5 = 20
Therefore, Jim had run 20 miles by the time he crossed paths with Tina.
To find the distance Jim ran by the time he crossed paths with Tina, we need to determine how long it took for them to meet. Since we know Tina's speed and the distance between their houses, we can calculate the time it took for Tina to reach Jim's house.
The formula to calculate time is:
Time = Distance / Speed
In this case, the distance is 5 miles, and Tina's speed is 10 miles per hour. Plugging these values into the formula, we get:
Time = 5 miles / 10 miles per hour
Time = 0.5 hours
So Tina took 0.5 hours to reach Jim's house.
Now that we know the time it took for Tina to reach Jim's house, we can calculate the distance Jim ran during that time. Jim's speed is 8 miles per hour, and the time is 0.5 hours. Using the same formula as before, we can find the distance:
Distance = Speed * Time
Distance = 8 miles per hour * 0.5 hours
Distance = 4 miles
Therefore, by the time Jim crossed paths with Tina, he had run 4 miles.