The distance between the two points X and Y is 160 km. A ship travels from X to Y downstream and then return from Y to X upstream and takes a total of 26 hrs for the whole journey. If the speed of the ship in still water is 13 km/hr, then, what is the speed of the current (in km/hr)?

Option 3 : 3

Given:

Distance between X and Y = 160 km

Time taken to cover downstream and upstream = 26 hrs

The speed of the boat in still water = 13 km/hr

Concept used:

Downstream Speed = Speed of Ship in still water + Speed of current

Upstream Speed = Speed of ship in still water – Speed of current

Calculation:

Suppose the speed of the current is x km/hr.

Downstream speed = (13 + x) km/hr

Upstream speed = (13 – x) km/hr

According to question –

⇒ 160/(13 + x) + 160/(13 – x) = 26

⇒ 160(13 – x + 13 + x) = 26(13 + x)(13 – x)

⇒ 160 × 2 × 13 = 26(169 – x²)

⇒ 160 = 169 – x²

⇒ x² = 169 – 160

⇒ x² = 9

⇒ x = √9

⇒ x = 3 km/hr