How Much Time Did the Cyclist Spend Cycling? Unlocking the Math Behind a 120 km Dual-Walk & Cycle Journey

If you’ve ever wondered how time is split when someone covers 120 km using equal walking and cycling segments—like cycling for part of the distance and walking the rest—this article breaks down the physics and math behind the scenario. In one compelling example, a cyclist covers 120 kilometers in exactly 4 hours, alternating cycling and walking. With cycling speed at 30 km/h and walking at 5 km/h, how many minutes did they spend actually cycling?

Understanding the Context

The Challenge: 120 km in 4 Hours with Equal Segments

Imagine a cyclist who splits their journey into two equal parts: 60 km cycling and 60 km walking, resulting in a total time of 4 hours. With cycling speed at 30 km/h, and walking at 5 km/h, we want to calculate the exact time spent cycling.

Step 1: Calculate Time Cycling and Walking in Equal Distances

A cyclist covers 120 km in 4 hours with equal walking and cycling segments. If cycling speed is 30 km/h and walking is 5 km/h, how many minutes did they spend cycling?

Key Insights

Let:

  • Distance cycled = 60 km
  • Distance walked = 60 km
  • Cycling speed = 30 km/h
  • Walking speed = 5 km/h

Time = Distance ÷ Speed

  • Time spent cycling = 60 km ÷ 30 km/h = 2 hours
  • Time spent walking = 60 km ÷ 5 km/h = 12 hours

Wait—this adds to 14 hours, not 4! So clearly, the equal distance assumption doesn’t match the time constraint.

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Final Thoughts

Step 2: Adjust for Total Time = 4 Hours

We know total time = 4 hours.
Let the distance cycled = x km
Then distance walked = 120 – x km

Time cycling = x ÷ 30
Time walking = (120 – x) ÷ 5

Total time:
(x/30) + ((120 – x)/5) = 4 hours

Now solve for x:

Multiply through by 30 to eliminate denominators:

x + 6(120 – x) = 120

Expand:
x + 720 – 6x = 120

Combine like terms:
-5x + 720 = 120

-5x = 120 – 720 = –600