A steamer goes downstream from one point another in 9 hours. It covers

1.	A steamer goes downstream from one point another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the steamer in still water and the distance between the ports.
Answer» Let the speed of steamer = x km/hr Speed of stream = 1 km/hr Downstream speed = (x + 1) km/hr Upstream speed = (x – 1) km/hr Distance = speed × time ⇒ 9 (x + 1) = 10 (x – 1)9 x + 9 = 10 x – 10x = 10 + 9 = 19 km/hr Therefore speed of the steamer is 19 km/hr Distance travelled = 9(x + 1) = 9 × 20 = 180 km.

A steamer goes downstream from one point another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the steamer in still water and the distance between the ports.

Answer»

Let the speed of steamer = x km/hr

Speed of stream = 1 km/hr

Downstream speed = (x + 1) km/hr

Upstream speed = (x – 1) km/hr

Distance = speed × time

⇒ 9 (x + 1)

= 10 (x – 1)9 x + 9

= 10 x – 10x

= 10 + 9 = 19 km/hr

Therefore speed of the steamer is 19 km/hr

Distance travelled = 9(x + 1) = 9 × 20 = 180 km.