All 6 problems from "Boats and Currents" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.
A boat's still-water speed is 22 km/h and the current is 3 km/h. Its downstream speed is ___ km/h.
Key idea: Downstream the current HELPS: boat speed + current. Upstream it FIGHTS: boat speed − current.
A boat's still-water speed is 22 km/h and the current is 3 km/h, travelling downstream.
Downstream the current pushes the boat along, so the speeds add.
Still-water speed 22 km/h, and the current adds 3 km/h.
22 + 3 = 25 km/h.
So: So the downstream speed is 25 km/h.
With the same boat (22 km/h) and current (3 km/h), the upstream speed is ___ km/h.
Key idea: Downstream the current HELPS: boat speed + current. Upstream it FIGHTS: boat speed − current.
The same boat (22 km/h) and current (3 km/h), now travelling upstream.
Upstream the current pushes against the boat, so it subtracts.
Still-water speed 22 km/h, and the current takes away 3 km/h.
22 − 3 = 19 km/h.
So: So the upstream speed is 19 km/h.
A ferry goes downstream at 28 km/h and returns upstream at 20 km/h. How fast is the current?
Key idea: Current = HALF the gap between the downstream and upstream speeds.
A ferry goes downstream at 28 km/h and returns upstream at 20 km/h.
The gap between the two speeds is the current counted twice — added one way, subtracted the other.
Gap: 28 − 20 = 8 km/h.
Current: 8 ÷ 2 = 4 km/h.
So: So the current is 4 km/h.
A boat's downstream speed is 30 km/h and its upstream speed is 18 km/h. Its still-water speed is ___ km/h.
Key idea: Still-water speed = the AVERAGE of the downstream and upstream speeds.
A boat's downstream speed is 30 km/h and its upstream speed is 18 km/h.
Still water sits exactly halfway between the helped speed and the hindered speed.
(30 + 18) ÷ 2 = 48 ÷ 2 = 24 km/h.
Check: current = (30 − 18) ÷ 2 = 6, and 24 + 6 = 30, 24 − 6 = 18.
So: So the still-water speed is 24 km/h.
A boat with still-water speed 24 km/h on a river with a 2 km/h current travels downstream for 3 hours. It covers ___ km.
Key idea: Distance = the real journey speed (with the current) × time.
Still-water speed 24 km/h, current 2 km/h, travelling downstream for 3 hours.
First get the real downstream speed, then multiply by the time.
Downstream speed: 24 + 2 = 26 km/h.
Distance: 26 × 3 = 78 km.
So: So it covers 78 km.
A boat (still-water speed 24 km/h, current 4 km/h) travels 84 km downstream. The trip takes ___ hours.
Key idea: Time = distance ÷ the real journey speed (with the current).
A boat (still-water 24 km/h, current 4 km/h) travels 84 km downstream.
Downstream speed first, then divide the distance by it.
Downstream speed: 24 + 4 = 28 km/h.
Time: 84 ÷ 28 = 3 hours.
So: So the trip takes 3 hours.
A boat travels at 20 km/h in still water. The river current flows at 4 km/h. Find the boat's speed downstream and upstream.
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
A boat travels at 20 km/h in still water. The river's current flows at 4 km/h. Same boat, same engine — why is one direction so much faster? The whole lesson answers that one question.
The engine gives the boat one speed; the river adds or takes away another — direction decides.
Change the numbers and watch the diagram redraw itself:
