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 be x km/hr. Speed of stream = 1 km/hr. Downstream speed = (x + 1) km/hr. Upstream speed = (x – 1) km/hr. By using the formula Distance = speed × time = (x + 1) × 9 and = (x – 1) × 10 9x + 9 = 10x – 10 9x – 10x = -10 -9 -x = -19 x = 19 km/hr. ∴ The speed of the steamer in still water is 19 km/hr. Distance between the ports is 9(x + 1) = 9(19+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 be x km/hr.

Speed of stream = 1 km/hr.

Downstream speed = (x + 1) km/hr.

Upstream speed = (x – 1) km/hr.

By using the formula

Distance = speed × time

= (x + 1) × 9 and

= (x – 1) × 10

9x + 9 = 10x – 10

9x – 10x = -10 -9

-x = -19

x = 19 km/hr.

∴ The speed of the steamer in still water is 19 km/hr.

Distance between the ports is 9(x + 1) = 9(19+1) = 9(20) = 180 km.