Question
M/J 18/P22/Q9 (a) On Monday, Ravi goes on a 20 km run. (i) His average speed for the first 12 km is \( x \mathrm{~km} / \mathrm{h} \). Write down an expression, in terms of \( x \), for the time taken for the first 12 km . Give your answer in minutes.
Ask by Edwards Tran. in Pakistan
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The time taken for the first 12 km is \( \frac{720}{x} \) minutes.
Solution
To determine the time Ravi takes to run the first 12 km at an average speed of \( x \) km/h, follow these steps:
1. **Formula for Time:**
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
2. **Plug in the Values:**
\[
\text{Time} = \frac{12 \text{ km}}{x \text{ km/h}} = \frac{12}{x} \text{ hours}
\]
3. **Convert Hours to Minutes:**
Since \( 1 \) hour equals \( 60 \) minutes:
\[
\frac{12}{x} \text{ hours} \times 60 \text{ minutes/hour} = \frac{720}{x} \text{ minutes}
\]
**Final Expression:**
\[
\frac{720}{x} \text{ minutes}
\]
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To find the time taken for the first 12 km at an average speed of \( x \) km/h, we can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] For the first 12 km, this becomes: \[ \text{Time} = \frac{12 \text{ km}}{x \text{ km/h}} = \frac{12}{x} \text{ hours}. \] Since the answer needs to be in minutes, we convert hours to minutes by multiplying by 60: \[ \text{Time in minutes} = \frac{12}{x} \times 60 = \frac{720}{x} \text{ minutes}. \] So, the expression for the time taken for the first 12 km in terms of \( x \) is \( \frac{720}{x} \) minutes.