Question

7. A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of strean be 2 km/h, find the speed of the steamer in still water and the distance between the points.​

Answer 1

Answer: Speed of the steamer in still water = 30 km/hr.

Distance between the ports = 224 km.

Step-by-step explanation:

Let the speed of the steamer in still water = x km/hr.

Given,

Speed of stream = 2 km/hr.

Downstream Speed = (x + 2) km/hr.

Upstream Speed = (x - 2) km/hr.

distance covered in 7 hours while downstream = 7(x + 2).

distance covered in 8 hours while upstream = 8(x - 2).

Now,

7(x + 2) = 8(x - 2)

7x + 14 = 8x - 16

7x - 8x = -16 - 14

-x = -30

x = 30.

Now,

∴ Distance between the ports = 7(x + 2) km

                                                = 7(30 + 2)

                                                = 7(32)

                                                = 224 km.

Therefore:

Speed of the steamer in still water = 30 km/hr.

Distance between the ports = 224 km.