Question

A group of three friends cycle from Llanfyllin to Vyrnwy at 12 km/h.
They then take the same amount of time to cycle from Vyrnwy
to Bala at 16 km/h.
What is their average speed for the journey from Llanfyllin to Bala?

Answer 1

The average speed for the journey from Llanfyllin to Bala is 14 km/h

Average speed is the ratio of total distance travelled to total time taken. Also, average speed can be given as the average of the different speeds.

Let d₁ represent the distance from Llanfyllin to Vyrnwy and t represent the time taken, since the speed is 12 km/h, hence:

12 = d₁/t

d₁ = 12t

Let d₂ represent the distance from Vyrnwy to bala and t represent the time taken. Since they spent the same time, since the speed is 16 km/h, hence:

16 = d₂/t

d₂ = 16t

Average speed = total distance/total time

Average speed = (d₁ + d₂) / (t + t)

Average speed = (12t + 16t) / 2t

Average speed = 28t / 2t

Average speed = 14 km/h

Hence their average speed for the journey from Llanfyllin to Bala is 14 km/h.

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