distance between any two cities is 192 km. Train A takes two hours les than train B. If the average speed of the train B is 16 km/hr. less than the average speed of the train . Find the average speed of each train.
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Total distance = 192 km
Let the average speed of the faster train = x km/h
So the average speed of the slower train= x-16 km/h
Time taken to cover 192 km by faster train = 192/x
Time taken to cover 192 km by slower train=192/x-16 km/h
According to the question
192/(x-16) - 192/x=2
192x-192(x-16)/x(x-16)=2
3072=2x^2-32x
x^2-16x-1536=0
x²-48x+32x-1536=0
x(x-48)+32(x-48)=0
(x-48)(x+32)=0
x= 48 , -32
Speed can't be negative.
So, x = 48 km/hr
Therefore the average speed of faster train=48km/h
and the average speed of slower train=48-16=32 km/h
Total distance = 192 km
Let the average speed of the faster train = x km/h
So the average speed of the slower train= x-16 km/h
Time taken to cover 192 km by faster train = 192/x
Time taken to cover 192 km by slower train=192/x-16 km/h
According to the question
192/(x-16) - 192/x=2
192x-192(x-16)/x(x-16)=2
3072=2x^2-32x
x^2-16x-1536=0
x²-48x+32x-1536=0
x(x-48)+32(x-48)=0
(x-48)(x+32)=0
x= 48 , -32
Speed can't be negative.
So, x = 48 km/hr
Therefore the average speed of faster train=48km/h
and the average speed of slower train=48-16=32 km/h
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