on a 100 M track A train travels the first 30 km at a uniform speed of 30 km per hour how fast must the train travel athe next 7O km so as to average 40 km per hour for the entire trip
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Total Distance = 100 KiloMetersCase 1:Distance = 30 KmSpeed = 30 kmphTime = Distance/Speed = 30/30 = 1 hour
Case 2:Distance = 70 KmLet Speed for this case be x kmphTime = distance/speed = 70/x hours
Now, Average speed for the entire journey is 40 kmphbut, average speed is given by total distance/total time = (30 + 70)/(1+70/x) = 100 / {(1x + 70)/x}.
=> 100/{(x + 70)/x} = 40=> 100 = 40[{x + 70}/x]=> 100 = (40x + 2800)/x=> 100x - 40x = 2800=> 60x = 2800=> x = 2800/60 = 46.66 kmph
Hence, the speed for the next 70 km should be 46.66 kmph so that the average speed for the entire journey is 40kmph....
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Case 2:Distance = 70 KmLet Speed for this case be x kmphTime = distance/speed = 70/x hours
Now, Average speed for the entire journey is 40 kmphbut, average speed is given by total distance/total time = (30 + 70)/(1+70/x) = 100 / {(1x + 70)/x}.
=> 100/{(x + 70)/x} = 40=> 100 = 40[{x + 70}/x]=> 100 = (40x + 2800)/x=> 100x - 40x = 2800=> 60x = 2800=> x = 2800/60 = 46.66 kmph
Hence, the speed for the next 70 km should be 46.66 kmph so that the average speed for the entire journey is 40kmph....
....hope this helps.....do rate and mark as brainiest if this helps you.....comment if you have any doubts.....
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