A train is moving at a speed of 80 km/h and covers a certain distance in 4.5 hours. The speed of the train to cover the same distance in 4 hours is

Options

A. A)100km/h
B. B)70 km/h
C. C)85km/h
D. D)90 km/h

Answer

To solve the problem step by step, we will use the relationship between distance, speed, and time.

### Step 1: Calculate the Distance Covered by the Train
We know that distance is calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed of the train (s1) = 80 km/h
- Time taken (t1) = 4.5 hours

Now, we can calculate the distance:
\[ \text{Distance} = 80 \, \text{km/h} \times 4.5 \, \text{h} \]
\[ \text{Distance} = 360 \, \text{km} \]

### Step 2: Set Up the Equation for the New Speed
Now, we need to find the new speed (s2) required to cover the same distance in a different time (t2).

Given:
- Time taken for the new speed (t2) = 4 hours

Using the same distance formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
We can set up the equation:
\[ 360 \, \text{km} = s2 \times 4 \, \text{h} \]

### Step 3: Solve for the New Speed (s2)
To find s2, we rearrange the equation:
\[ s2 = \frac{360 \, \text{km}}{4 \, \text{h}} \]
\[ s2 = 90 \, \text{km/h} \]

### Final Answer
The speed of the train to cover the same distance in 4 hours is **90 km/h**.

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