Question

By what percent will the time of travel increase or decrease if the speed is decreased

by 25% and the total distance is increased by 50%?

Answer 1

The time of travel will increase by 100% if the speed decreases by 25% and the distance increases by 50%, as the new time is twice the original time.

Step-by-step explanation:

The student is asking about the relationship between speed, distance, and time, which involves algebraic calculations.

To find how the time of travel will change if speed decreases by 25% and distance increases by 50%, we can use the formula Time = Distance / Speed.

Let's assume the original speed is S and the original distance is D.

The new speed would be 0.75S (a reduction of 25%) and the new distance would be 1.5D (an increase of 50%).

Therefore, the original time (T) is D / S, while the new time (Tnew) is 1.5D / 0.75S, which simplifies to 2D / S, or twice the original time.

So, the time of travel will increase by 100%.

Answer 2

The time of travel will increase by 100% when the speed is decreased by 25% and the distance is increased by 50%, meaning the travel time will double.

Step-by-step explanation:

To calculate the percentage increase or decrease in travel time when the speed is reduced by 25% and the distance is increased by 50%, we can use the concept of inverse proportionality between speed and time, and direct proportionality between distance and time. When speed decreases, time increases; and when distance increases, time also increases.

The original speed can be represented as 'S', and the new speed after a 25% reduction is 0.75S. Similarly, if the original distance is 'D', the new distance after a 50% increase is 1.5D. The time to travel a distance is equal to the distance divided by the speed.

Original time taken (T) = D / S

New time taken (T') = New Distance / New Speed = 1.5D / 0.75S = (1.5/0.75) * (D/S) = 2 * T

Therefore, the new time taken is twice the original time. This means that the time of travel will increase by 100%, doubling, as a result of the combined effect of decreasing the speed by 25% and increasing the distance by 50%.