To solve this problem, we need to determine the point where the paths of the two runners cross. At this point, both runners will be at the same distance from the flagpole. We can use the following steps to solve the problem:
1. Calculate the time it takes for the runners to cross paths:
- Let d be the distance between the runners when they start running.
- The relative speed of the runners is the sum of their speeds, which is (8.4 + 7.8) km/h = 16.2 km/h.
- The time it takes for the runners to cross paths is t = d / (16.2 km/h).
- We can use the following equation to calculate d: d = (5.3 km + 5.0 km) + (8.4 km/h) * t + (-7.8 km/h) * t
- Simplifying the equation, we get: d = 10.3 km - 0.6 km/h * t
2. Substitute the value of t into the equation for d to find the distance between the runners when they cross paths:
- From step 1, we know that t = d / (16.2 km/h).
- Substituting this into the equation for d, we get: d = 10.3 km - 0.6 km/h * (d / 16.2 km/h)
- Simplifying the equation, we get: d = 10.3 km - 0.037 km * d 1.037 km * d = 10.3 km
d = 9.93 km
3. Calculate the distance of each runner from the flagpole when they cross paths:
- Runner A is 5.3 km west of the flagpole, so the distance from the flagpole is 5.3 km + (9.93 km / 2) = 10.265 km.
- Runner B is 5.0 km east of the flagpole, so the distance from the flagpole is 5.0 km + (9.93 km / 2) = 10.465 km.
Therefore, when their paths cross, Runner A is approximately 10.265 km from the flagpole, and Runner B is approximately 10.465 km from the flagpole...
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