Question

In an 8.00 km race, one runner runs at a steady 11.0 km/h and another runs at 14.0 km/h. How far from the finish line is the slower runner when the faster runner finishes the race?

Answer 1

The slower runner is approximately 0.003 km (or 3 meters) away from the finish line when the faster runner finishes the race.

Step-by-step explanation:

To find the distance from the finish line for the slower runner when the faster runner finishes the race, we can use the formula: Distance = Speed × Time. Let's assume the slower runner is 'X' km away from the finish line when the faster runner finishes. The faster runner takes T hours to finish the race, so the faster runner covers a distance of 11T km. At the same time, the slower runner takes T + ΔT hours and covers a distance of 8 - X km. Since both runners are running at a steady speed, their speed will remain constant throughout the race. Therefore, we can set up the equation: 11T = 8 - X.

Simplifying the equation, we get: X = 8 - 11T. Now, we can substitute the value of T from the above equation into this equation to find X. Let's assume T = 0.727 hours (which is approximately 43.64 minutes, calculated by dividing the distance 8 km by the speed of the faster runner, 11 km/h). Substituting this value, we get: X = 8 - 11(0.727) = 8 - 7.997 = 0.003 km.

Therefore, the slower runner is approximately 0.003 km (or 3 meters) away from the finish line when the faster runner finishes the race.