Module 1 · Arithmetic
Chapter 11: Boats & Streams
Arithmetic
3 topics
What this chapter covers
The 3 topics below make up Boats & Streams on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Effective speeds & recovery
| Downstream speed | D = b + s |
|---|---|
| Upstream speed | U = b − s |
| Still-water (boat) speed | b = (D + U) / 2 |
| Stream (current) speed | s = (D − U) / 2 |
| Time = Distance ÷ speed | t = d / (b ± s) |
Round trips & ratios
| Round-trip average speed | 2·D·U / (D + U) (harmonic mean) |
|---|---|
| b : s from times (same distance) | b : s = (t↑ + t↓) : (t↑ − t↓) |
| b : s from distances (equal time) | b : s = (d↓ + d↑) : (d↓ − d↑) |
| Total time for distance d each way | d/(b+s) + d/(b−s) |
| Still-water vs stream time ratio | t_still : t_against = (b−s) : b |
CAT reference
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