Boats and Streams with Relative Speed Logic | Banking Quant Mastery - Study Chapter | QuizMaker

Treat upstream and downstream speed as combinations of still-water speed and stream speed.

Read: 3m
Type: Chapter
Access: Free

Course

Banking Quant Mastery: Arithmetic to Data Sufficiency

Topic

Module 3: Work, Motion and Rates

Why This Chapter Matters

Boat questions are just relative-speed questions with current added in. Once still-water speed and stream speed are separated cleanly, upstream, downstream, ratio, and time-comparison problems become routine.

Core Ideas

Downstream speed $= b + s$ , upstream speed $= b - s$ , where $b$ is still-water speed and $s$ is stream speed.
Still-water speed $=downstream+upstream2=\frac{\text{downstream}+\text{upstream}}{2}$ .
Stream speed $=downstream−upstream2=\frac{\text{downstream}-\text{upstream}}{2}$ .
Round-trip questions usually ask for total time, so solve each leg separately.
If the time for equal distances upstream and downstream is given, compare speeds through reciprocals rather than forcing a long equation immediately.

High-Value Formulas

Concept	Formula / Rule
Downstream	$d = b + s$
Upstream	$u = b - s$
Still-water speed	$b=d+u2b=\frac{d+u}{2}$
Stream speed	$s=d−u2s=\frac{d-u}{2}$
Equal-distance total time	$T=xb+s+xb−sT=\frac{x}{b+s}+\frac{x}{b-s}$

How To Approach Questions

Define still-water and stream speeds first.
Convert the verbal condition into upstream or downstream time.
For back-and-forth travel, compute both times separately and add.
If a ratio is given between upstream and downstream speeds, express both in the same variable first.

Worked Examples

Example 1

Prompt: If downstream speed is $km/h14\text{ km/h}$ and upstream speed is $km/h7\text{ km/h}$ , find the still-water speed.

Approach: Still-water speed $km/h=\frac{14+7}{2}=10.5\text{ km/h}$ .

Example 2

Prompt: A boat covers $42$ km downstream and returns the same distance upstream with speeds $14$ and $7$ km/h respectively. Find the total time.

Approach: Time $=4214+427=3+6=9=\frac{42}{14}+\frac{42}{7}=3+6=9$ hours.

Example 3

Prompt: A boat covers $160$ km downstream in half the time taken for the same distance upstream. If the downstream speed is found from $96$ km in $3$ hours, find the stream speed.

Approach: Downstream speed is $km/h32\text{ km/h}$ . If upstream takes double the time for the same distance, then upstream speed is half, so $km/h16\text{ km/h}$ . Stream speed $km/h=\frac{32-16}{2}=8\text{ km/h}$ .

Common Mistakes

Using downstream formula for the upstream leg.
Averaging speeds directly in a round-trip time problem.
Forgetting that stream speed is half the difference between downstream and upstream speeds.
Mixing still-water speed with downstream speed inside the same step.

Quick Revision

Boat questions become stable once every sentence is rewritten in terms of still-water speed, stream speed, and direction.