Final answer:
To prove that a 25% increase in average speed results in a 20% reduction in time taken, we use the relationship Speed = Distance / Time. The original time multiplied by 0.8 (after speed increases by 25%) denotes a 20% reduction in time.
Step-by-step explanation:
To show that on any journey, if the average speed is increased by 25%, the time taken for the journey is reduced by 20%, we can use the basic relationship between speed, distance, and time. This relationship is expressed in the formula: Speed = Distance / Time. Let's denote the original average speed as V and the original time taken as T. If we increase the average speed to 1.25V (an increase of 25%), the new time taken T' becomes the distance (which remains the same) divided by the new speed, yielding T' = Distance / (1.25V). But since the original time T was the distance divided by V, we can write T' = T / 1.25. This simplifies to T' = 0.8T, showing a reduction of 20% in time, since 0.8 is equivalent to 80% of the original time T.