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On a 60 km straight road , a bus travels the rest 30 km with a uniform speed of 30km/h . How fast must the bus travels the next 30 km as to have average speed of 40 km/h for the entire trip?
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On a 60 km straight road , a bus travels the rest 30 km with a uniform...
Problem:
On a 60 km straight road, a bus travels the rest 30 km with a uniform speed of 30km/h. How fast must the bus travels the next 30 km as to have an average speed of 40 km/h for the entire trip?
Solution:
Understanding the problem:
The problem requires us to calculate the speed at which the bus must travel for the next 30 km to have an average speed of 40 km/h for the entire trip. We also know that the bus has already traveled 30 km at a speed of 30 km/h.
Calculating the total time:
Let's calculate the total time taken by the bus to travel the entire 60 km:
Time taken to travel the first 30 km = Distance/Speed = 30/30 = 1 hour
Let the speed of the bus for the next 30 km be x km/h.
Time taken to travel the next 30 km = Distance/Speed = 30/x
Total time taken to travel the entire 60 km = 1 + 30/x hours
Calculating the average speed:
The average speed of the entire trip is given by:
Average speed = Total distance/Total time
Average speed = 60/(1 + 30/x)
Calculating the required speed:
Now, we need to find the value of x, which will make the average speed of the entire trip equal to 40 km/h. Therefore, we can write:
40 = 60/(1 + 30/x)
1 + 30/x = 60/40 = 3/2
30/x = 1/2
x = 60 km/h
Answer:
Therefore, the speed at which the bus must travel for the next 30 km to have an average speed of 40 km/h for the entire trip is 60 km/h.
Community Answer
On a 60 km straight road , a bus travels the rest 30 km with a uniform...
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On a 60 km straight road , a bus travels the rest 30 km with a uniform speed of 30km/h . How fast must the bus travels the next 30 km as to have average speed of 40 km/h for the entire trip?
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