Calculating Average Speed for the Journey

The average speed is calculated by dividing the total distance travelled by the total time taken. The formula is:

$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $

Step 1: Calculate Distance for Each Part

First, calculate the distance covered during each part of the journey using the formula: Distance = Speed × Time.

• Part 1 Distance:

  Speed = 20 m/min

  Time = 90 min

  $ \text{Distance}_1 = 20 \, \text{m/min} \times 90 \, \text{min} = 1800 \, \text{m} $

• Part 2 Distance:

  Speed = 70 m/min

  Time = 60 min

  $ \text{Distance}_2 = 70 \, \text{m/min} \times 60 \, \text{min} = 4200 \, \text{m} $

Step 2: Calculate Total Distance and Total Time

Next, sum the distances and times from both parts.

• Total Distance:

  $ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 1800 \, \text{m} + 4200 \, \text{m} = 6000 \, \text{m} $

• Total Time:

  $ \text{Total Time} = 90 \, \text{min} + 60 \, \text{min} = 150 \, \text{min} $

Step 3: Calculate Average Speed

Finally, use the total distance and total time to find the average speed.

$ \text{Average Speed} = \frac{6000 \, \text{m}}{150 \, \text{min}} = 40 \, \text{m/min} $

Conclusion

The average speed for the entire journey is 40 m/min.