Practice Questions
Concept Explanation
Upstream and downstream problems find boat speed in still water and stream speed from timed journeys with and against the current.
Key Formulas
- Downstream speed = Still water speed + Stream speed
- Upstream speed = Still water speed − Stream speed
- Still water speed = (Downstream + Upstream) / 2
- Stream speed = (Downstream − Upstream) / 2
Example
30 km downstream in 2 h and 30 km upstream in 3 h. Downstream = 15 km/h, upstream = 10 km/h. Boat = 12.5 km/h; stream = 2.5 km/h.
Common Trap
Compute downstream and upstream speeds from distance/time first, then apply the half-sum and half-difference formulas.
-
Q1 EasyA boat covers 30 km downstream in 2 hours and the same distance upstream in 3 hours. What is the speed of the boat downstream?ExplanationDownstream = 30/2 = 15 km/h.
-
Q2 EasyA boat covers 30 km downstream in 2 hours and the same distance upstream in 3 hours. What is the speed of the boat upstream?ExplanationUpstream = 30/3 = 10 km/h.
-
Q3 EasyA boat covers 30 km downstream in 2 hours and the same distance upstream in 3 hours. What is the speed of the stream?ExplanationStream = (15 − 10)/2 = 2.5 km/h.
-
Q4 EasyA boat can travel at 10 km/h in still water and the speed of the stream is 2 km/h. How long will the boat take to cover 48 km downstream?ExplanationDownstream = 12 km/h. Time = 48/12 = 4 hours.
-
Q5 EasyThe downstream speed of a boat is 20 km/h and its upstream speed is 12 km/h. What is the speed of the boat in still water?ExplanationBoat = (20 + 12)/2 = 16 km/h.
-
Q6 EasyThe downstream speed of a boat is 18 km/h and its upstream speed is 14 km/h. What is the speed of the stream?ExplanationStream = (18 − 14)/2 = 2 km/h.
-
Q7 EasyA boat can travel at 14 km/h in still water and the speed of the stream is 3 km/h. What is the downstream speed of the boat?ExplanationDownstream = 14 + 3 = 17 km/h.
-
Q8 MediumA boat covers 30 km downstream in 2 hours and the same distance upstream in 3 hours. What is the speed of the boat in still water?ExplanationBoat = (15 + 10)/2 = 12.5 km/h.
-
Q9 MediumA boat covers 24 km downstream in 1.5 hours and the same distance upstream in 2 hours. What is the speed of the stream?ExplanationDown = 16 km/h, up = 12 km/h. Stream = (16 − 12)/2 = 2 km/h.
-
Q10 MediumA boat can travel at 12 km/h in still water and the speed of the stream is 3 km/h. How long will the boat take to cover 45 km upstream?ExplanationUpstream = 9 km/h. Time = 45/9 = 5 hours.
-
Q11 MediumA boat covers 40 km downstream in 2 hours and the same distance upstream in 4 hours. What is the speed of the stream?ExplanationDown = 20 km/h, up = 10 km/h. Stream = (20 − 10)/2 = 5 km/h.
-
Q12 MediumA boat can travel at 15 km/h in still water and the speed of the stream is 5 km/h. How long will the boat take to cover 60 km upstream?ExplanationUpstream = 10 km/h. Time = 60/10 = 6 hours.
-
Q13 HardA boat can travel at 8 km/h in still water and the speed of the stream is 2 km/h. The boat travels 20 km downstream and then returns 20 km upstream. What is the total time for the round trip?ExplanationDown 20/10 = 2 h; up 20/6 ≈ 3.33 h. Total ≈ 5.33 h ≈ 5.5 h.
-
Q14 HardA boat covers 36 km downstream in 3 hours and the same distance upstream in 4.5 hours. What is the speed of the boat in still water?ExplanationDown = 12 km/h, up = 8 km/h. Boat = (12 + 8)/2 = 10 km/h.
-
DS1 Easy
A boat travels on a river. What is the downstream speed of the boat?
Statement IThe boat covers 30 km downstream in 2 hours.
Statement IIThe boat covers 30 km upstream in 3 hours.
ExplanationStatement I alone: 30/2 = 15 km/h. -
DS2 Easy
What is the speed of a boat in still water?
Statement IThe downstream speed of the boat is 15 km/h.
Statement IIThe upstream speed of the boat is 10 km/h.
ExplanationBoat = (15 + 10)/2 = 12.5 km/h.
-
DS3 Easy
What is the speed of the stream in which a boat is travelling?
Statement IThe downstream speed of the boat is 20 km/h.
Statement IIThe upstream speed of the boat is 12 km/h.
ExplanationStream = (20 − 12)/2 = 4 km/h. -
DS4 Medium
How long will a boat take to cover 48 km downstream on a river?
Statement IThe speed of the boat in still water is 10 km/h.
Statement IIThe speed of the stream is 2 km/h.
ExplanationDownstream = 12 km/h. Time = 48/12 = 4 hours.