If a man can row upstream 30 km and downstream 45 km in the same time and the speed of the boat is 4 km/hr more than the speed of the stream, then find the speed of the stream and time taken to complete the total journey.

Option 4 : 1 km/hr and 15 hours

**Given:**

Distance travelled in upstream (D_{U}) = 30 km

Distance travelled in downstream (D_{D}) = 45 km

Time taken in both cases is same i.e. T_{D} = T_{U}

Speed of boat in still water = (4 + speed of stream) km/hr

**Formula used:**

Downstream speed (S_{D}) = Speed of boat + Speed of stream

Upstream speed (S_{U}) = Speed of boat – Speed of stream

TD = DD/SD

Where TD, DD, and SD are time, distance and speed respectively during downstream

TU = DU/SU

Where TU, DU, and SU are time, distance and speed respectively during upstream

**Solution:**

Let the speed of boat be x km/hr and speed of stream = y km/hr

⇒ x = (y + 4) km/hr (Given)

S_{D} = x + y

⇒ S_{D} = y + 4 + y

⇒ S_{D} = 2y +4

S_{U} = x – y

⇒ S_{U} = y + 4 – y

⇒ S_{U} = 4 km/hr

T_{D} = T_{U}

⇒ D_{D}/S_{D} = D_{U}/S_{U}

⇒ 45/(2y + 4) = 30/4

⇒ 2y + 4 = 6

⇒ **y = 1 km/hr**

⇒ x = y + 4 = 5 km/hr

⇒ T_{U} = 30/4

⇒ T_{U} = 7.5 hours = T_{D}

⇒ Total time = T_{U} + T_{D} = 7.5 + 7.5 = **15 hours**

**∴**** Speed of stream is 1 km/hr and total time taken is 15 hours**