Question

A long distance runner running a 5km track is pacing himself by running 4.5km/h at 9km/h and the rest at 12.5km/h9

Answer 1

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.

Given the following data;

• 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;

$Time \ A = \frac {Distance \; A}{Speed \; A}$

Substituting the values into the formula, we have;

$Time \ A = \frac {4.5}{9.5}$

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;

$Time \ B = \frac {0.5}{12.5}$

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;

$Average \; speed = \frac {total \; distance}{total \; time}$

$Average \; speed = \frac {5}{0.5137}$

Average speed = 9.7333 km/h