PRELIMINARY STAGE 2025
Ofori Panin SHS: 79 points
Kpando SHS: 40 points
Awe SHTS: 20 points
QUESTION
A student cycles 2 km in 15 minutes, rests for 5 minutes, then cycles 1.5 km in 10 minutes.
What is the average speed of the student, expressed in km/h?
ANSWER: 7 km/h
SOLUTION:
Find the total distance:
$2+1.5=3.5\text{ km}$
Find the total time, including the rest:
$15+5+10=30\text{ min}$
$30\text{ min}=0.5\text{ h}$
Find the average speed:
$\dfrac{3.5}{0.5}=7\text{ km/h}$
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PRACTICE QUESTIONS
1. QUESTION: A student cycles 2.5 km in 12 minutes, rests for 6.0 minutes, then cycles 1.5 km in 12 minutes. What is the average speed of the student in km/h?
ANSWER: 8.0 km/h
SOLUTION:
$\text{total distance} = 2.5 + 1.5$
$\text{total distance} = 4.0\text{ km}$
$\text{total time} = 12 + 6.0 + 12$ (the rest counts)
$\text{total time} = 30.0\text{ min}$
$30.0\text{ min} = \dfrac{30.0}{60}\text{ h}$
$30.0\text{ min} = \dfrac{1}{2}$
$30.0\text{ min} = 0.5\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{4.0}{0.5}$
$v_{\text{avg}} = \dfrac{4}{5\times10^{-1}}$
$v_{\text{avg}} = \dfrac{4}{5} \times10^{1}$
$v_{\text{avg}} = 8.0\text{ km/h}$
2. QUESTION: A student cycles 3.0 km in 15 minutes, rests for 5.0 minutes, then cycles 2.4 km in 16 minutes. What is the average speed of the student in km/h?
ANSWER: 9.0 km/h
SOLUTION:
$\text{total distance} = 3.0 + 2.4$
$\text{total distance} = 5.4\text{ km}$
$\text{total time} = 15 + 5.0 + 16$ (the rest counts)
$\text{total time} = 36.0\text{ min}$
$36.0\text{ min} = \dfrac{36.0}{60}\text{ h}$
$36.0\text{ min} = \dfrac{3}{5}$
$36.0\text{ min} = 0.6\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{5.4}{0.6}$
$v_{\text{avg}} = \dfrac{54}{6}$
$v_{\text{avg}} = 9.0\text{ km/h}$
3. QUESTION: A student cycles 6.0 km in 25 minutes, rests for 5.0 minutes, then cycles 3.6 km in 18 minutes. What is the average speed of the student in km/h?
ANSWER: 12 km/h or $1.2\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 6.0 + 3.6$
$\text{total distance} = 9.6\text{ km}$
$\text{total time} = 25 + 5.0 + 18$ (the rest counts)
$\text{total time} = 48.0\text{ min}$
$48.0\text{ min} = \dfrac{48.0}{60}\text{ h}$
$48.0\text{ min} = \dfrac{4}{5}$
$48.0\text{ min} = 0.8\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{9.6}{0.8}$
$v_{\text{avg}} = \dfrac{96}{8}$
$v_{\text{avg}} = 12\text{ km/h}$
4. QUESTION: A student cycles 1.8 km in 8.0 minutes, rests for 4.0 minutes, then cycles 1.2 km in 12 minutes. What is the average speed of the student in km/h?
ANSWER: 7.5 km/h
SOLUTION:
$\text{total distance} = 1.8 + 1.2$
$\text{total distance} = 3.0\text{ km}$
$\text{total time} = 8.0 + 4.0 + 12$ (the rest counts)
$\text{total time} = 24.0\text{ min}$
$24.0\text{ min} = \dfrac{24.0}{60}\text{ h}$
$24.0\text{ min} = \dfrac{2}{5}$
$24.0\text{ min} = 0.4\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{3.0}{0.4}$
$v_{\text{avg}} = \dfrac{3}{4\times10^{-1}}$
$v_{\text{avg}} = \dfrac{3}{4} \times10^{1}$
$v_{\text{avg}} = 7.5\text{ km/h}$
5. QUESTION: A student cycles 3.5 km in 14 minutes, rests for 7.0 minutes, then cycles 4.3 km in 15 minutes. What is the average speed of the student in km/h?
ANSWER: 13 km/h or $1.3\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 3.5 + 4.3$
$\text{total distance} = 7.8\text{ km}$
$\text{total time} = 14 + 7.0 + 15$ (the rest counts)
$\text{total time} = 36.0\text{ min}$
$36.0\text{ min} = \dfrac{36.0}{60}\text{ h}$
$36.0\text{ min} = \dfrac{3}{5}$
$36.0\text{ min} = 0.6\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{7.8}{0.6}$
$v_{\text{avg}} = \dfrac{78}{6}$
$v_{\text{avg}} = 13\text{ km/h}$
6. QUESTION: A student cycles 6.5 km in 25 minutes, rests for 5.0 minutes, then cycles 4.0 km in 15 minutes. What is the average speed of the student in km/h?
ANSWER: 14 km/h or $1.4\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 6.5 + 4.0$
$\text{total distance} = 10.5\text{ km}$
$\text{total time} = 25 + 5.0 + 15$ (the rest counts)
$\text{total time} = 45.0\text{ min}$
$45.0\text{ min} = \dfrac{45.0}{60}\text{ h}$
$45.0\text{ min} = \dfrac{3}{4}$
$45.0\text{ min} = 0.75\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{10.5}{0.75}$
$v_{\text{avg}} = \dfrac{105\times10^{-1}}{75\times10^{-2}}$
$v_{\text{avg}} = \dfrac{7}{5} \times10^{1}$
$v_{\text{avg}} = 14\text{ km/h}$
7. QUESTION: A student cycles 2.2 km in 9.0 minutes, rests for 4.0 minutes, then cycles 1.1 km in 5.0 minutes. What is the average speed of the student in km/h?
ANSWER: 11 km/h or $1.1\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 2.2 + 1.1$
$\text{total distance} = 3.3\text{ km}$
$\text{total time} = 9.0 + 4.0 + 5.0$ (the rest counts)
$\text{total time} = 18.0\text{ min}$
$18.0\text{ min} = \dfrac{18.0}{60}\text{ h}$
$18.0\text{ min} = \dfrac{3}{10}$
$18.0\text{ min} = 0.3\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{3.3}{0.3}$
$v_{\text{avg}} = \dfrac{33}{3}$
$v_{\text{avg}} = 11\text{ km/h}$
8. QUESTION: A student cycles 4.8 km in 16 minutes, rests for 8.0 minutes, then cycles 4.2 km in 12 minutes. What is the average speed of the student in km/h?
ANSWER: 15 km/h or $1.5\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 4.8 + 4.2$
$\text{total distance} = 9.0\text{ km}$
$\text{total time} = 16 + 8.0 + 12$ (the rest counts)
$\text{total time} = 36.0\text{ min}$
$36.0\text{ min} = \dfrac{36.0}{60}\text{ h}$
$36.0\text{ min} = \dfrac{3}{5}$
$36.0\text{ min} = 0.6\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{9.0}{0.6}$
$v_{\text{avg}} = \dfrac{9}{6\times10^{-1}}$
$v_{\text{avg}} = \dfrac{3}{2} \times10^{1}$
$v_{\text{avg}} = 15\text{ km/h}$
9. QUESTION: A student cycles 2.1 km in 6.0 minutes, rests for 3.0 minutes, then cycles 2.4 km in 6.0 minutes. What is the average speed of the student in km/h?
ANSWER: 18 km/h or $1.8\times10^{1}$ km/h
SOLUTION:
$\text{total distance} = 2.1 + 2.4$
$\text{total distance} = 4.5\text{ km}$
$\text{total time} = 6.0 + 3.0 + 6.0$ (the rest counts)
$\text{total time} = 15.0\text{ min}$
$15.0\text{ min} = \dfrac{15.0}{60}\text{ h}$
$15.0\text{ min} = \dfrac{1}{4}$
$15.0\text{ min} = 0.25\text{ h}$
$v_{\text{avg}} = \dfrac{\text{total distance}}{\text{total time}}$
$v_{\text{avg}} = \dfrac{4.5}{0.25}$
$v_{\text{avg}} = \dfrac{45\times10^{-1}}{25\times10^{-2}}$
$v_{\text{avg}} = \dfrac{9}{5} \times10^{1}$
$v_{\text{avg}} = 18\text{ km/h}$