A car covers 30km at a uniform speed of 30km/h. What should be its speed for the next 90km if the average speed for the entire journey is 60km/h? Explain in detail.




The problem states that a car covers a distance of 30km at a uniform speed of 30km/h. We need to determine the speed at which the car should travel for the next 90km, in order to maintain an average speed of 60km/h for the entire journey.


To find the speed of the car for the next 90km, let's first calculate the time taken for the initial 30km using the formula: Time = Distance / Speed.

Given:
Distance = 30km
Speed = 30km/h

Substituting the values:
Time = 30km / 30km/h = 1 hour


Now, let's calculate the total time taken for the entire journey. We know that the average speed is given by the formula: Average Speed = Total Distance / Total Time.

Given:
Average Speed = 60km/h
Total Distance = 30km + 90km = 120km

Rearranging the formula to find the total time:
Total Time = Total Distance / Average Speed

Substituting the values:
Total Time = 120km / 60km/h = 2 hours


We have the total time taken for the entire journey as 2 hours. Since the time taken for the initial 30km is 1 hour, the time remaining for the next 90km is 2 hours - 1 hour = 1 hour.

To find the speed for the next 90km, we can use the formula: Speed = Distance / Time.

Given:
Distance = 90km
Time = 1 hour

Substituting the values:
Speed = 90km / 1 hour = 90km/h


Therefore, in order to maintain an average speed of 60km/h for the entire journey, the car should travel at a speed of 90km/h for the next 90km.

45km/h