Final answer:
To calculate the percent decrease in distance when the speed is decreased by 25% and the time is decreased by 50%, we can use the distance formula and the percent decrease formula. The distance will decrease by 62.5%.
Step-by-step explanation:
To calculate the percent decrease in distance, we need to first understand the relationship between speed, time, and distance. The formula to calculate distance is:
Distance = Speed x Time
Let's assume the initial speed is represented by S and the initial time is represented by T. We are given that the speed is decreased by 25%, so the new speed is 0.75S (75% of the initial speed). The time is decreased by 50%, so the new time is 0.5T (50% of the initial time).
Using the distance formula, we can calculate the initial distance (D1) and the new distance (D2):
D1 = S x T
D2 = 0.75S x 0.5T = 0.375ST
To calculate the percent decrease in distance, we can use the following formula:
Percent decrease = ((D1 - D2) / D1) x 100
Substituting the values, we get:
Percent decrease = ((S x T - 0.375ST) / (S x T)) x 100
Simplifying the equation further, we get:
Percent decrease = (1 - 0.375) x 100 = 62.5%