Shortcut Trick
Downstream Speed = 15.5 + 4.5 = 20 km/h
Upstream Speed = 15.5 − 4.5 = 11 km/h
Total Time = (76 ÷ 20) + (104.5 ÷ 11)
Total Time = 3.8 + 9.5 = 13.3 hours
13.3 hours = 13 hours and (0.3 × 60) minutes = 13 hours 18 minutes.
∴ The correct answer is 13 hours 18 minutes.
Alternate Method
Given:
Speed of the boat in still water (vb) = 15.5 km/h
Speed of the stream (vs) = 4.5 km/h
Distance covered downstream (Dd) = 76 km
Distance covered upstream (Du) = 104.5 km
Formula Used:
Downstream Speed = vb + vs
Upstream Speed = vb − vs
Time = Distance ÷ Speed
Downstream: 76 km at 20 km/h → 3.8 h
Upstream: 104.5 km at 11 km/h → 9.5 h
Total Time = 3.8 h + 9.5 h = 13.3 h
Calculations:
⇒ Downstream Speed = 15.5 + 4.5 = 20 km/h
⇒ Upstream Speed = 15.5 − 4.5 = 11 km/h
⇒ Time taken to travel downstream = 76 ÷ 20 = 3.8 hours
⇒ Time taken to travel upstream = 104.5 ÷ 11 = 9.5 hours
⇒ Total time taken for the journey = 3.8 + 9.5 = 13.3 hours
⇒ Converting to hours and minutes = 13 hours + (0.3 × 60) minutes = 13 hours 18 minutes
∴ The correct answer is 13 hours 18 minutes.
Additional Information
Downstream and Upstream Speeds
When a boat moves with the flow of the river, it is called downstream, and Speed = Boat Speed + Stream Speed. When moving against the flow, it is upstream, and Speed = Boat Speed − Stream Speed.
Calculating Individual Speeds
If the downstream speed is D and the upstream speed is U, then Boat Speed in Still Water = (D + U) ÷ 2 and Speed of the Stream = (D − U) ÷ 2.
Average Speed for Equal Distances
If a boat covers a certain distance downstream and the exact same distance upstream, its average speed is given by (2 × D × U) ÷ (D + U).