A motorist travels a certain distance x in five hours at an average speed of 90km/h.what average speed must she maintain to cover the distance in 4 hours?
distance = speed * time = 5*90 = 450 km/hr
speed = distance/time = 450/4 = 112.5 km/hr
Or, you can reason like this: 4/5 the time means 5/4 the speed. 5/4 * 90 = 112.5
To find the average speed the motorist must maintain to cover the distance in 4 hours, we can use the formula:
Average Speed = Distance / Time
We know that the distance traveled, x, is the same in both scenarios. We also know the time it takes in each scenario: 5 hours for the distance x, and 4 hours for the same distance.
Let's use these values to calculate the average speed the motorist must maintain to cover the distance in 4 hours:
Given:
Distance (x) = x
Time (t1) = 5 hours
Average Speed (v1) = 90 km/h
We can calculate the average speed for the first scenario using the formula:
v1 = x / t1
Rearranging the formula, we have:
x = v1 * t1
Now, we want to find the average speed for the second scenario:
Time (t2) = 4 hours
We can use the same formula to find the average speed for the second scenario:
v2 = x / t2
Substituting the value of x from the first scenario:
v2 = (v1 * t1) / t2
Substituting the given values:
v2 = (90 km/h * 5 hours) / 4 hours
Simplifying:
v2 = 450 km/h / 4 hours
v2 = 112.5 km/h
Therefore, the motorist must maintain an average speed of 112.5 km/h to cover the distance in 4 hours.