Final answer:
To find when the runners will cross paths, calculate the time it takes for them to meet using the equation d=rt. The two runners will cross paths approximately 35 minutes and 17 seconds after they start running towards each other.
Step-by-step explanation:
To find when the two runners will cross paths, we can use the equation d=rt. Since Runner A and Runner B are running towards each other, their total distance should be equal to the initial distance between them. Runner A is traveling at a rate of 4/5 mph, and Runner B is traveling at a rate of 13 mph. They are initially 2 miles apart.
Let's assume t is the time it takes for them to meet. Runner A will cover a distance of (4/5)*t miles, and Runner B will cover a distance of 13*t miles.
Setting up the equation (4/5)*t + 13*t = 2, we can solve for t.
Combining like terms, we get (4/5+13)*t = 2.
Simplifying further, we have (17/5)*t = 2.
To isolate t, we divide both sides by (17/5). This gives us t = (2*5)/17 = 10/17 hours.
Since we need the answer in minutes, we multiply t by 60 to convert it to minutes. t = (10/17)*60 = 35.29 minutes, which is approximately 35 minutes and 17 seconds