Question

The car is moving at a constant rate. 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

Step-by-step explanation:

Might be easiest to pick some numbers

distance = 100 mi

speed = 20 mi/hr

time needed at 20 mi/hr = 5 hr

Now change distance to 150 mi and speed to 15 mi/hr

now time req is 150 /15 = 10 hrs = 100% increase from 5 hr

Or here is another way :

t1 = distance / rate now change the distance to 1.5 distance and rate to .75 rate :

t2 = 1.5 distance / .75 rate = 2 * distance/rate = 2 x t1 or double the time which is a 100% increase in time required .

Answer 2

If a car's speed is decreased by 25% and the distance is increased by 50%, the travel time doubles, which is an increase of 100% compared to the original time.

Step-by-step explanation:

When the speed of a car is decreased by 25%, the new speed becomes 0.75 times the original speed. If the total distance is increased by 50%, the new distance is 1.5 times the original distance. To find out by what percent the time of travel will increase or decrease, we can use the formula Time = Distance / Speed. Let's assume the original time to travel the original distance at the original speed is t hours.

Initially, we have Time = Distance / Speed. So the new time after changes will be New Time = (1.5 × Distance) / (0.75 × Speed) = Time × (1.5 / 0.75) = Time × 2. Hence, the travel time doubles, which is an increase of 100% compared to the original travel time.