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A-Level Mathematics Question Analysis - Mathematics - Exponentials

A-Level Mathematics Question Analysis

· A-Level Maths,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
⇒ (432 + 24x - 432 + 24x)/[(18 - x)(18 + x)] = 1
⇒ 48x = 324 - x2
⇒ x2 + 48x − 324 = 0
⇒ x2 + 54x − 6x − 324 = 0
⇒ x(x + 54) − 6(x + 54) = 0
⇒ (x + 54)(x − 6) = 0

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

As such, the stream's speed is 6 km / h.

Work hard for your A-Level Mathematics examination!

End of analysis. Great!

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