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Solving challenging 2023 PSLE Maths questions: Faizal and Elise Jogging question
When it comes to mastering challenging maths problems, the 2023 Primary School Leaving Examination (PSLE) has certainly set the bar high. One such challenging question that has been a topic of discussion among students and educators alike is the "Faizal and Elise's Jogging Question."
In this article, we will delve into the details of this problem, providing a comprehensive solution that will help you understand how to solve such questions.
PSLE 2023 Faizal and Elise jogging question on speed
Question:
Faizal and Elise started jogging from the same spot at the same time. Faizal's speed was \(30 \text{ m/min}\) faster than that of Elise's. Both of them did not change their speed throughout the jog. Faizal jogged all the way to the end of the track and immediately made a U-turn. They passed each other at the \(\text{4000-m}\) mark of the track. What was Elise's speed?
The question also included a diagram (As seen above) illustrating that Faizal ran an additional \(\text{600 meters}\) before turning back and covering the same distance before overtaking Elise.
Solution:
Let's look at the question. What information do we have?
- Faizal and Elise started jogging from the same spot at the same time.
- Faizal's speed was \(30 \text{ m/min}\) faster than that of Elise's. Or, for every minute that Elise jogged, Faizal ran \(\text{30 meters}\) more than her.
- Neither Faizal nor Elise changed the speed throughout their jog.
- Faizal jogged all the way to the end of the track and immediately made a U-turn. They passed each other at the \(\text{4000-m}\) mark of the track.
After knowing all of this, we are required to solve what was Elise's speed.
Do you remember your Speed-Distance-Time formula? It's time to apply it to this question.
We know that \(\displaystyle{\mathrm{Speed= \frac{Distance}{Time}}}\).
So, to find Elise's speed, we need to know:
- The distance that she covered.
- The time she took to run.
Now, let's look at the question again.
"They passed each other at the \(\text{4000-m}\) mark of the track"
This means that Elise had jogged for \(\text{4000 meters}\) when Faizal passed her.
Now this is where the question becomes tricky. The question does not tell us the time Elise took to reach this \(\text{4000-m}\) mark.
Let's look for clues from the question.
We know that Faizal's speed was \(30 \text{ m/min}\) faster than that of Elise.
We also know that Faizal ran \(\text{600 m}\) one way, turned around and ran \(\text{600 m}\) before he passed Elise.
This means that Faizal ran \(\text{1200 meters}\) more than Elise \((600\times2=1200)\) in the amount of time that Elise took to run \(\text{4000 meters}\).
Now, to find how much time Faizal took to jog, we need to calculate \(\displaystyle{\mathrm{\frac{Distance}{Time}}}\).
Which is \(\displaystyle{\mathrm{{1200\over30}=40}}\) minutes.
This means, Faizal took \(\text{40 minutes}\) to run \(\text{1200 m}\).
So, Elise must have taken \(\text{40 minutes}\) to reach the same point!
Now, we have the time Elise took to run \(\text{4000 m}\).
Putting all of the information in the formula \(\displaystyle{\mathrm{Speed= \frac{Distance}{Time}}}\).
Elise's Speed \(\displaystyle{= \mathrm{4000\over 40} = 100 \text{ m/min}}\)
That's it, we have our answer!
Elise's speed is \(100 \text{ m/min}\).
