A-Level Mathematics Question Analysis - Mathematics - Exponentials

A-Level Mathematics Question Analysis Topic: Mathematics - Exponentials

Exam Question:

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer:

For A-Level Mathematics, you should know:

First, we will need to let the stream's speed be x km / h.

Then, some brainstorming:
1) The speed of the boat in still water is 18 km / h (given).
2) Its speed upstream is (18 - x) km / h.
3) Its speed downstream is (18 + x) km / h.

We also know that the distance between the places is 24 km.

Then, define a few more terms:
4) The time taken to travel upstream would be d / (18 - x) hours.
5) Downstream would be d / (18 + x) hours.

Calculating, we know that the upstream journey time = downstream journey time + 1 hour (since difference between both times amounts to one hour)

$In\; other\; words,24\; /\; (18\; -\; x)\; =\; 24\; /\; (18\; +\; x)\; +\; 1\Rightarrow \; (432\; +\; 24x\; -\; 432\; +\; 24x)/[(18\; -\; x)(18\; +\; x)]\; =\; 1\Rightarrow \; 48x\; =\; 324\; -\; x2\Rightarrow \; x2 +\; 48x\; -\; 324\; =\; 0\Rightarrow \; x2 +\; 54x\; -\; 6x\; -\; 324\; =\; 0\Rightarrow \; x(x\; +\; 54)\; -\; 6(x\; +\; 54)\; =\; 0\Rightarrow \; (x\; +\; 54)(x\; -\; 6)\; =\; 0$

$From\; this,\; we\; have:x\; =\; -54\; (rejected\; since\; speed\; cannot\; be\; negative),\; x\; =\; 6$

$As\; such,\; the\; stream\text{'}s\; speed\; is\; 6\; km\; /\; h.$

Work hard for your A-Level Mathematics examination!

End of analysis. Great!

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