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Question
A train travels the first 30km of its journey at 30km/h. Find the speed it should travel the next 90km to have an average speed of 60km/h.
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Solution
The train travels the first 30 km at speed of 30 km/hr.
Time taken by train to cover this distance is = distance/speed = 30/30 = 1 hr.
Let the speed of the train to cover the next 90 km is v.
Then time taken by train to cover this 90 km is 90/v.
Total time becomes T = 1 +90/v = ( v + 90)/v.
Total distance= 120 km.
Average speed = 60 km/h (given)
However average is given by = total distance /total time.
So (120 x v)/(v +90) = 60
120 v = 60v +5400
60v = 5400
v= 5400/60 =90 km/hr.
so train has to cover those 90 km at a speed of 90 km/hr.
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