. A train covers a distance of 180 k.m. at a uniform speed. If the spe

1.	. A train covers a distance of 180 k.m. at a uniform speed. If the speed hadbeen 9 k.m./Hr more, It would have taken 1 hour less for the same journey.Find the speed of the train.
Answer» Let speed of train is v1Time taken at v speed is t1 If speed increased by 9v2 = v1 + 9Time taken at increased speedt2 = t1 - 1 As distance remains same v1t1 = v2t2v1t1 = (v1+9)(t1-1)v1t1 = v1t1 - v1 + 9t1 - 9v1 = 9(t1 - 1).....(1) Distance = speedtime180 = 9(t1-1)t1t1^2 - t1 - 20 = 0t1^2 - 5t1 + 4t1 - 20 = 0t1(t1 - 5) +4(t1 - 5) = 0t1 = 5, - 4 Put value of t1 in eq(1)v1 = 9(5-1)v1 = 94 = 36 km/hr Speed of train is 36 km/hr

. A train covers a distance of 180 k.m. at a uniform speed. If the speed hadbeen 9 k.m./Hr more, It would have taken 1 hour less for the same journey.Find the speed of the train.

Answer»

Let speed of train is v1Time taken at v speed is t1

If speed increased by 9v2 = v1 + 9Time taken at increased speedt2 = t1 - 1

As distance remains same

v1*t1 = v2*t2v1*t1 = (v1+9)(t1-1)v1*t1 = v1*t1 - v1 + 9t1 - 9v1 = 9(t1 - 1).....(1)

Distance = speed*time180 = 9(t1-1)*t1t1^2 - t1 - 20 = 0t1^2 - 5t1 + 4t1 - 20 = 0t1(t1 - 5) +4(t1 - 5) = 0t1 = 5, - 4

Put value of t1 in eq(1)v1 = 9(5-1)v1 = 9*4 = 36 km/hr

Speed of train is 36 km/hr