A train running at 7/11 of its own speed reached a place in 22 hours. How much time could be saved if the train would have run at its own speed ?

Options

A. 14 hours
B. 7 hours
C. 8 hours
D. 16 hours

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the variables
Let the normal speed of the train be \( S \) (in hours).

### Step 2: Calculate the effective speed
The train is running at \( \frac{7}{11} \) of its normal speed. Therefore, the effective speed of the train is:
\[ \text{Effective Speed} = \frac{7}{11} S \]

### Step 3: Calculate the distance traveled
The train takes 22 hours to reach its destination at this effective speed. Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
we can substitute the values:
\[ \text{Distance} = \left(\frac{7}{11} S\right) \times 22 \]
Calculating this gives:
\[ \text{Distance} = \frac{154}{11} S = 14 S \]

### Step 4: Calculate the time taken at normal speed
If the train were to travel this same distance at its normal speed \( S \), we can use the distance formula again:
\[ \text{Time at normal speed} = \frac{\text{Distance}}{\text{Normal Speed}} = \frac{14 S}{S} = 14 \text{ hours} \]

### Step 5: Calculate the time saved
Now, we can find out how much time would be saved if the train traveled at its normal speed instead of the reduced speed:
\[ \text{Time saved} = \text{Time taken at reduced speed} - \text{Time taken at normal speed} \]
Substituting the values:
\[ \text{Time saved} = 22 \text{ hours} - 14 \text{ hours} = 8 \text{ hours} \]

### Conclusion
The time that could be saved if the train had run at its own speed is **8 hours**.

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