A train is travelling at the rate of 45km/hr. How many seconds it will takes to cover a distance of `(4)/(5)km`?

Options

A. 36 sec
B. 64 sec
C. 90sec
D. 120 sec

Answer

To solve the problem step by step, we need to find out how many seconds it will take for a train traveling at a speed of 45 km/hr to cover a distance of \( \frac{4}{5} \) km.

### Step 1: Convert the distance from kilometers to meters.
1 km = 1000 meters, so:
\[ \frac{4}{5} \text{ km} = \frac{4}{5} \times 1000 \text{ m} = 800 \text{ m} \]

### Step 2: Convert the speed from kilometers per hour to meters per second.
To convert km/hr to m/s, we use the conversion factor:
\[ 1 \text{ km/hr} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{1}{3.6} \text{ m/s} \]
Thus, for 45 km/hr:
\[ 45 \text{ km/hr} = 45 \times \frac{1000}{3600} \text{ m/s} = 45 \times \frac{5}{18} \text{ m/s} = \frac{225}{18} \text{ m/s} = 12.5 \text{ m/s} \]

### Step 3: Use the formula for distance to find time.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Rearranging the formula to find time gives us:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{800 \text{ m}}{12.5 \text{ m/s}} = 64 \text{ seconds} \]

### Final Answer:
The train will take **64 seconds** to cover a distance of \( \frac{4}{5} \) km.

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