Complete Question:
A long distance runner running a 5.0km track is pacing himself by running 4.5km at 9.0km/hr and the rest at 12.5km/hr. What is the average speed?
Answer:
Average speed = 9.7333 km/h
Explanation:
- Let the total distance be divided into A and B.
<u>Given the following data;</u>
- Total distance = 5 km
- Distance A = 4.5 km
- Speed A = 9.5 km/hr
- Speed B = 12.5 km/hr
To find the average speed;
First of all, we would determine the time taken to cover distance A in speed A by using the formula;
![Time \ A = \frac {Distance \; A}{Speed \; A}](https://tex.z-dn.net/?f=%20Time%20%5C%20A%20%3D%20%5Cfrac%20%7BDistance%20%5C%3B%20A%7D%7BSpeed%20%5C%3B%20A%7D%20)
Substituting the values into the formula, we have;
![Time \ A = \frac {4.5}{9.5}](https://tex.z-dn.net/?f=%20Time%20%5C%20A%20%3D%20%5Cfrac%20%7B4.5%7D%7B9.5%7D%20)
Time A = 0.4737 hours
Total distance = distance A + distance B
5 = 4.5 + distance B
Distance B = 5 - 4.5
Distance B = 0.5 Km
Next, we would determine the time to cover distance B in speed B;
![Time \ B = \frac {0.5}{12.5}](https://tex.z-dn.net/?f=%20Time%20%5C%20B%20%3D%20%5Cfrac%20%7B0.5%7D%7B12.5%7D%20)
Time A = 0.04 hours
Total time = time A + time B
Total time = 0.4737 + 0.04
Total time = 0.5137 hours
Now, we would solve for the average speed;
Mathematically, the average speed of an object is given by the formula;
![Average \; speed = \frac {total \; distance}{total \; time}](https://tex.z-dn.net/?f=%20Average%20%5C%3B%20speed%20%3D%20%5Cfrac%20%7Btotal%20%5C%3B%20distance%7D%7Btotal%20%5C%3B%20time%7D%20)
![Average \; speed = \frac {5}{0.5137}](https://tex.z-dn.net/?f=%20Average%20%5C%3B%20speed%20%3D%20%5Cfrac%20%7B5%7D%7B0.5137%7D%20)
<em>Average speed = 9.7333 km/h</em>