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Practice sheet · Swimming Path · Lens 1: Math

Pools & pace

Practice for The Math of Swimming: pool area and volume, Pythagoras, currents, pace and splits, pressure, drowning data and stroke rate (pp.8–16), plus Algebra A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Volume = length × width × depth; 1 m³ = 1,000 L. A sloped floor: use the average depth. Speed = distance ÷ time; pace = time per 100 m.

Pressure p = ρgh = 1,000 × 9.8 × depth (Pa). Currents add as vectors at right angles. Swim where a lifeguard is on duty, and wear a lifejacket in boats and open water.

Warm-up

One step

Area, volume and splits.
1

Pool deck

A pool is 25 m by 15 m. What is its surface area and its perimeter?

2

Fill it

The pool is 1.8 m deep all over. What is its volume in m³ and in litres?

3

Splits

A swimmer’s 50 m splits are 34, 36, 37 and 35 seconds. What is the 200 m time in minutes and seconds? The average split?

4

Deep end

What is the water pressure 3 m down (on top of air pressure)?

Core

Two or three steps

Sketch the pool or river first.
5

Sloped floor

A 25 m by 10 m pool slopes evenly from 1 m deep to 3 m. What is its volume?

6

Diagonal

How long is the corner-to-corner diagonal of a 25 m by 15 m pool?

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Swimming Path · Unizon · PracticeArea, volume & pace
7

River current

A swimmer heads straight across a 36 m river at 0.9 m/s. The current flows at 1.2 m/s. Find the real speed, the time to cross, how far downstream they land and the angle off straight across.

8

Pace

An 800 m swim takes 14:40. What is the average speed in m/s, and the pace per 100 m?

9

Stroke rate

A swimmer takes 36 strokes a minute and travels 1.75 m per stroke. What is the speed in m/min and m/s?

10

Drowning data

Alberta had 44 water-related deaths in 2024. Using the 2020–24 pattern of 26% in lakes and 31% in rivers, about how many were in lakes? In rivers and lakes together?

Level Up

Equations

A1–A2 (pp.17–18).
11

Fill time

A pool holds 200,000 L and a hose adds 25,000 L an hour. Solve 200,000 + 25,000t = 700,000.

12

Pass or pay?

Drop-in costs $7 a visit. A pass is $50 plus $2.50 a visit. Solve 7v = 50 + 2.5v. From how many visits is the pass cheaper?

13

Platform

From a 7.2 m platform, h = 7.2 − 5t². When does a diver reach the water?

14

Deck border

A 12 m by 20 m pool gets a deck of even width x. The pool and deck cover 384 m². Solve (12 + 2x)(20 + 2x) = 384.

Make your own problem

Your turn to be the lifeguard

  1. Pick a pool, lake or river you know.
  2. Write a question about its area, volume, a swimmer’s pace or a current.
  3. Solve it, then add one safety rule the numbers support.

My problem, and my worked answer:

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Swimming Path · Unizon · PracticeArea, volume & pace

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Drowning figures: Lifesaving Society Alberta snapshot (p.15). Swim with a lifeguard on duty.

Warm-up
1
375 m² · 80 m 25 × 15 = 375; 2 × (25 + 15) = 80.
2
675 m³ · 675,000 L 25 × 15 × 1.8 = 675; × 1,000 L.
3
2:22 · 35.5 s 34 + 36 + 37 + 35 = 142 s = 2 min 22 s; 142 ÷ 4 = 35.5.
4
29,400 Pa 1,000 × 9.8 × 3 = 29,400 Pa, about 29 kPa.
Core
5
500 m³ Average depth (1 + 3) ÷ 2 = 2 m: 25 × 10 × 2 = 500.
6
≈ 29.2 m √(25² + 15²) = √850 ≈ 29.2.
7
1.5 m/s · 40 s · 48 m · ≈ 53.1° √(0.9² + 1.2²) = 1.5. 36 ÷ 0.9 = 40 s; 1.2 × 40 = 48 m; tan⁻¹(1.2 ÷ 0.9) ≈ 53.1°. Never swim across a real river: currents are often faster.
8
≈ 0.91 m/s · 1:50 per 100 m 14:40 = 880 s; 800 ÷ 880 ≈ 0.91; 880 ÷ 8 = 110 s = 1:50.
9
63 m/min · 1.05 m/s 36 × 1.75 = 63; 63 ÷ 60 = 1.05.
10
≈ 11 · ≈ 25 0.26 × 44 ≈ 11; 0.57 × 44 ≈ 25. Both percents are of the same 100%, so they can be added (p.15).
Level Up
11
20 hours 25,000t = 500,000 → t = 20.
12
≈ 11.1 · from 12 visits 4.5v = 50 → v ≈ 11.1. At 12 visits: $84 vs $80.
13
1.2 s 5t² = 7.2 → t² = 1.44 → t = 1.2.
14
x = 2 m At x = 2: 16 × 24 = 384. (The other root is negative.)
Make your own: sketch it, use the average depth for slopes, and keep metres, litres and seconds labelled.
Swimming Practice · Swimming Path · UnizonAnswer key