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!