Sure, let's go through each question step-by-step:
### Question 26:
A man riding his bicycle covers 125 meters in 35 seconds. We need to determine his speed in kilometers per hour.
1. Calculate the speed in meters per second:
The formula for speed is:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
- Distance = 125 meters
- Time = 35 seconds
So,
[tex]\[
\text{Speed} = \frac{125}{35} \approx 3.5714285714285716 \text{ meters per second}
\][/tex]
2. Convert the speed to kilometers per hour:
To convert from meters per second (m/s) to kilometers per hour (km/hr), we use the conversion factor:
[tex]\[
1 \text{ meter per second} = 3.6 \text{ kilometers per hour}
\][/tex]
Therefore,
[tex]\[
\text{Speed in km/hr} = 3.5714285714285716 \times 3.6 \approx 12.85714285714286 \text{ km/hr}
\][/tex]
3. Find the closest answer in the given options:
The correct answer in the form of [tex]\( km/hr \)[/tex] and given in fractional format is:
[tex]\[
12 \frac{2}{7}
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{12 \frac{2}{7}}
\][/tex]
### Question 27:
Every floor of a 30-storey building is 6 meters high. We need to determine the time it takes for a lift moving at 3 meters per second to move from the 4th floor to the 25th floor.
1. Calculate the number of floors the lift needs to travel:
- Initial floor = 4th floor
- Final floor = 25th floor
The number of floors to travel:
[tex]\[
\text{Floors to travel} = 25 - 4 = 21 \text{ floors}
\][/tex]
2. Calculate the total distance traveled by the lift:
Each floor is 6 meters high, so:
[tex]\[
\text{Total distance} = 21 \times 6 = 126 \text{ meters}
\][/tex]
3. Calculate the time taken at the speed of the lift:
The speed of the lift is given as 3 meters per second.
Using the formula:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
[tex]\[
\text{Time} = \frac{126}{3} = 42 \text{ seconds}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{42 \text{ sec}}
\][/tex]
By following these steps, we find the solutions to both questions accurately.
