A journey of 192 km from Mumbai to Pune takes 2 hours less by a superfasttrain than that by an ordinary passenger train. If the average speed ofthe slower train is 16 km/h less that that of the faster train, determinetheir a average speeds.
Let average speed of fast train = x
Therefore, average speed of slow train = x – 16
192x = 192(x – 16) + 2x(x – 16) 192x = 192x – 3072 + 2x 2 – 32x
– 3072 + 2x 2 – 32x = 0
2x 2 – 32x – 3072 = 0
x 2 – 16x – 1536 = 0
x 2 – 48x + 32x – 1536 = 0
x(x – 48) + 32(x – 48) = 0
(x + 32)(x – 48) = 0
(x + 32) = 0 or (x – 48) = 0
x = -32 or x = 48
Therefore the average speed of the fast train = 48 km/hr
and the speed of the slow train = x – 16 = 32 km/hr.
Checking:
6 = 4 + 2
6 = 6.
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