1. For how long did Eze travel 10 km at the speed of $$ 20 \mathrm{~km} / \mathrm{hr} $$ ? (N.C.E.E 2011) [a] 60 min . [b] 30 min . [c] 15 min [d] 10 min [e] 2 min 2. $$ \mathrm{A}, \mathrm{B} $$ and $$ C $$ are three houses in this order along a street in Lagos. The distance from $$ A $$ to $$ B $$ is 120 m and the distance from $$ B $$ to $$ C $$ is two-third of that of A and B. What is the distance between A and C? (N.C.E.E 2011) [a] 360 m [b] 240 m [c] 200 m [d] 80 m [e] 40 m An athlete runs $$ q \mathrm{~km} $$ in t hour. His speed is (N.C.E.E 2009) [a] qt km per hour [b] $$ \frac{q}{t} \mathrm{~km} $$ per hour c] $$ t \mathrm{~km} $$ per hour $$ \mathrm{q}[\mathrm{d}](q-t) \mathrm{km} $$ per hour ] $$ (q+t) \mathrm{km} $$ per hour

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Let's address each question one by one:

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**1. For how long did Eze travel 10 km at the speed of $$ 20 \mathrm{~km} / \mathrm{hr} $$?**  
**Options:**  
[a] 60 min  
[b] 30 min  
[c] 15 min  
[d] 10 min  
[e] 2 min

**Solution:**  
Time is calculated using the formula:
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{10 \, \text{km}}{20 \, \text{km/hr}} = 0.5 \, \text{hours}
$$
Convert hours to minutes:
$$
0.5 \, \text{hours} \times 60 \, \text{min/hr} = 30 \, \text{minutes}
$$

**Answer:**  
**[b] 30 min**

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**2. $$ A $$, $$ B $$, and $$ C $$ are three houses in this order along a street in Lagos. The distance from $$ A $$ to $$ B $$ is 120 m and the distance from $$ B $$ to $$ C $$ is two-thirds of that of $$ A $$ to $$ B $$. What is the distance between $$ A $$ and $$ C $$?**  
**Options:**  
[a] 360 m  
[b] 240 m  
[c] 200 m  
[d] 80 m  
[e] 40 m

**Solution:**  
Distance from $$ B $$ to $$ C $$:
$$
\frac{2}{3} \times 120 \, \text{m} = 80 \, \text{m}
$$
Total distance from $$ A $$ to $$ C $$:
$$
120 \, \text{m} + 80 \, \text{m} = 200 \, \text{m}
$$

**Answer:**  
**[c] 200 m**

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**3. An athlete runs $$ q \mathrm{~km} $$ in $$ t $$ hours. His speed is:**  
**Options:**  
[a] $$ qt $$ km per hour  
[b] $$ \frac{q}{t} $$ km per hour  
[c] $$ t $$ km per hour  
[d] $$ q - t $$ km per hour  
[e] $$ q + t $$ km per hour

**Solution:**  
Speed is calculated using the formula:
$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{q \, \text{km}}{t \, \text{hr}} = \frac{q}{t} \, \text{km/hr}
$$

**Answer:**  
**[b] $$ \frac{q}{t} $$ km per hour**

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**1. Eze traveled for 30 minutes.** **2. The distance between A and C is 200 meters.** **3. The athlete's speed is $$ \frac{q}{t} $$ km per hour.**

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