on a 120km track, a train travels the first30km at a uniform speed of 30km/h. How fastmust the train travel the next 90km so as toaverage 60km/h for the entire trip.
Question
on a 120km track, a train travels the first30km at a uniform speed of 30km/h. How fastmust the train travel the next 90km so as toaverage 60km/h for the entire trip.
Solution
To solve this problem, we first need to understand that the average speed is calculated by dividing the total distance by the total time.
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Calculate the time taken to travel the first 30km at 30km/h: Time = Distance/Speed = 30km / 30km/h = 1 hour
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Calculate the total time taken to travel 120km at an average speed of 60km/h: Time = Distance/Speed = 120km / 60km/h = 2 hours
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Subtract the time taken to travel the first 30km from the total time to find the time left to travel the next 90km: Time left = Total time - Time for first 30km = 2 hours - 1 hour = 1 hour
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Calculate the speed needed to travel the next 90km in the time left: Speed = Distance/Time = 90km / 1 hour = 90km/h
So, the train must travel at a speed of 90km/h for the next 90km to average 60km/h for the entire trip.
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