Without any stoppage, a person travels a certain distance at an average speed of 42 km/h. When stoppages are included, he covers the same distance at an average speed of 28 km/h. For how many minutes in each hour does he stop?

Introduction / Context:
This question is about average speed with and without stoppages. It is a standard type of problem in time, speed and distance, where you are asked to relate the effective average speed including rest stops to the actual running speed. The goal is to understand how much time per hour is lost due to stoppages based on the reduction in average speed.

Given Data / Assumptions:

The person travels at an average speed of 42 km/h when there are no stoppages.
Including stoppages, the average speed for the same distance reduces to 28 km/h.
The running speed when in motion is assumed to remain 42 km/h.
We must find how many minutes out of each hour are spent stopping.

Concept / Approach:
Average speed including stoppages is equal to total distance divided by total time, where total time includes both running time and stoppage time. Since the running speed is constant at 42 km/h, the ratio of effective average speed to running speed gives the fraction of time actually spent moving. The remaining fraction of each hour represents stoppage time. We express this fraction of an hour in minutes to get the final answer.

Step-by-Step Solution:
Step 1: Compare effective average speed with running speed. Running speed = 42 km/h, effective average speed including stops = 28 km/h. Fraction of time spent moving = effective average speed / running speed. So, fraction of time moving = 28 / 42 = 2 / 3. Step 2: Compute the fraction of time stopped. Total time in one hour is represented by 1. Fraction of time stopped = 1 - 2 / 3 = 1 / 3. Step 3: Convert this fraction of an hour into minutes. One hour = 60 minutes. Stoppage time per hour = (1 / 3) * 60 minutes = 20 minutes.

Verification / Alternative Check:
We can also reason using a simple distance, for example 42 km. If he runs without stopping, 42 km at 42 km/h takes 1 hour. With stoppages, his average is 28 km/h, so to cover 42 km he needs 42 / 28 = 1.5 hours. That means he spent 1 hour actually running and 0.5 hour stopping. Half an hour is 30 minutes, but that is total stoppage for 42 km. Per hour of clock time, the stoppage fraction is still one third of the time, which corresponds to 20 minutes per hour. The direct fraction method is cleaner and avoids confusion.

Why Other Options Are Wrong:
Option 15 minutes corresponds to a stoppage fraction of 1/4 hour, which would give a different effective speed ratio not equal to 28 / 42.
Option 18 minutes is 0.3 hour, which again does not match the ratio 2 / 3 for moving time.
Option 22 minutes is an awkward number and does not fit any simple fraction that would reproduce the correct speed reduction from 42 km/h to 28 km/h.

Common Pitfalls:
Students often confuse distance ratio with time ratio and may incorrectly try to subtract speeds. Another mistake is choosing an arbitrary distance and getting lost in calculation instead of directly using the simple ratio effective speed / running speed. Forgetting to convert the fraction of an hour into minutes correctly is another frequent source of error.

Final Answer:
The person stops for 20 minutes in each hour.