Warda walks at an average speed of 3 km/hr for 45 minutes before running for half an hour at a certain average speed $u$. If she travels a total distance of 5 km, calculate the average running speed.

1. Problem Description

Warda walks at an average speed of 3 km/hr for 45 minutes before running for half an hour at a certain average speed $u$. If she travels a total distance of 5 km, calculate the average running speed.

2. Solution Steps

First, we need to convert the walking time to hours. 45 minutes is equal to $45/60 = 0.75$ hours.

Next, we calculate the distance covered while walking.

$Distance = Speed \times Time$

Distance covered while walking $= 3 \text{ km/hr} \times 0.75 \text{ hr} = 2.25 \text{ km}$.

The total distance traveled is 5 km. The distance covered while running is the total distance minus the distance covered while walking.

Distance covered while running $= 5 \text{ km} - 2.25 \text{ km} = 2.75 \text{ km}$.

The time spent running is half an hour, which is $0.5$ hours.

To find the average running speed, we use the formula:

$Speed = Distance / Time$

Average running speed $u = 2.75 \text{ km} / 0.5 \text{ hr} = 5.5 \text{ km/hr}$.

Table:

| Activity | Speed (km/hr) | Time (hr) | Distance (km) |

|---|---|---|---|

| Walking | 3 | 0.75 | 2.25 |

| Running | 5.5 | 0.5 | 2.75 |

| Total | - | 1.25 | 5 |

3. Final Answer

The average running speed is 5.5 km/hr.