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 stream be 2 km/hr, find the speed of the steamer in still water and the distance between the ports.

Solution:

Given, a steamer goes downstream from one point to another in 7 hours.

The steamer covers the same distance upstream in 8 hours.

The speed of stream is 2 km/hr

We have to find the speed of the steamer in still water and the distance between the ports.

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

Downstream speed = (x+2) km/hr

Upstream speed = (x-2) km/hr

We know, distance = speed × time

Distance covered downstream in 7 hours = (x+2) × 7

= 7x + 14 km

Distance covered upstream in 8 hours = (x-2) × 8

= 8x - 16 km

According to the question,

7x + 14 = 8x - 16

7x - 8x = -16 - 14

-x = -30

x = 30 km/hr

Therefore, speed of steamer in still water is 30 km/hr.

Total distance = 7x + 14

= 7(30) + 14

= 210 + 14

= 224 km

Therefore, the distance between the ports is 224 km.

✦ Try This: A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of stream be 5 km/hr, find the speed of the steamer in still water and the distance between the ports.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 2

NCERT Exemplar Class 8 Maths Chapter 4 Sample Problem 9

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 stream be 2 km/hr, find the speed of the steamer in still water and the distance between the ports

Summary:

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 the stream is 2 km/hr, the speed of the steamer in still water and the distance between the ports are 30 km/hr and 224 km.

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