Question

A steamer goes downstream from one point to another in 7 hours, it covers the same distance upstream in 8 hours. If speed of the stream be 2km/hr, find the speed of the steamer in still water and the distance between the ports.

Please answer

Answer 1

Answer:

30 km/hr, 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.

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

Given, 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.

Hope it helps!

Answer 2

Step-by-step explanation:

speed of stream = 2 km/hr

let speed of boat (in still water) = x km/hr

while going downstream  his speed = x+2 km/hr

and going upstream = x-2 km/hr

now A/Q

dis /x+2 = 7⇒ dis = 7 (x+2)  ......(1)

and dis / x-2 = 8 ⇒ dis = 8(x-2)  ............(2)

(1) =  (2)

7x + 14= 8x - 16  ⇒ x = 30 km/hr

and dis = 7(30+2) = 7 x 32 = 224 km