Question

A motor boat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hrs 30 mins. The speed of the stream (in km/hr) is:-
1. 5 km/hr.
2. 10 km/hr.
3. 15 km/hr.
4. 20 km/hr.
5. 25 km/hr.

Answer 1

Correct Answer - Option 1 : 5 km/hr.

Given:

Speed in still water = 15 km/hr

Total distance = 30 km

Total time = 4 hrs 30 mins = 412 hr = 9/2 hr.

Formula used:

Distance = Speed × Time 

Calculation:

Let the speed of the of the stream be X km/hr

Speed upstream = (15 – X) km/hr

Speed downstream = (15 + X) km/hr 

According to question:

⇒ [30/(15 + x) + 30/(15 – X)] = 9/2

⇒ (450 – 30X + 450 + 30X) / (15 + X) × (15 – X) = 9/2

⇒ 900 = [(152 – X2) × 9/2]

⇒ (900 × 2/9) = 225 – X2

⇒ X2 = 225 – 200

⇒ X2 = 25

⇒ x = 5

∴ Speed of the stream is 5 km/hr.

If the speed of boat or swimmer is X km/hr and the speed of the stream is y km/hr then,

Speed of boat upstream = (X – Y) km/hr.

Speed of boat downstream = (X + Y) km/hr.