If Suraj travels at 8/9th of his usual speed, he misses a train by 10 minutes. But if he travels
at 5/4th of his usual speed, he reaches the station 5 minutes before the departure of the
train. What is the approximate normal time taken by Suraj to reach the railway station?
A. 1 hour 4 minutes
B. 52 minutes
C. 37 minutes
D. 46 minutes

Let Suraj's usual speed be \( S \), and let the normal time taken to reach the station be \( T \). The distance between his starting point and the station is constant, so we can use the relationship between speed, time, and distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

### Case 1: Speed is \( \frac{8}{9}S \)
In this case, Suraj is late by 10 minutes. If his speed is \( \frac{8}{9}S \), the time taken is \( \frac{9}{8}T \), and he is 10 minutes late, so:
\[
\frac{9}{8}T = T + 10
\]
Simplifying:
\[
\frac{9}{8}T - T = 10
\]
\[
\frac{1}{8}T = 10
\]
\[
T = 80 \text{ minutes}
\]

### Case 2: Speed is \( \frac{5}{4}S \)
In this case, Suraj reaches 5 minutes early. If his speed is \( \frac{5}{4}S \), the time taken is \( \frac{4}{5}T \), and he is 5 minutes early, so:
\[
\frac{4}{5}T = T - 5
\]
Simplifying:
\[
T - \frac{4}{5}T = 5
\]
\[
\frac{1}{5}T = 5
\]
\[
T = 25 \times 5 = 80 \text{ minutes}
\]

### Conclusion:
The normal time taken by Suraj to reach the station is \( 80 \) minutes, which is equivalent to **1 hour 20 minutes**.

So, the correct answer should be **none of the provided options** as they are not correct for this specific problem. However, based on similar problems or rounding errors, the expected answer might be closest to **1 hour 4 minutes (A)**.

Would you like further clarification or details? Here are some related questions to think about:

1. How would the problem change if the distance were doubled?
2. Can this problem be solved using a graphical approach?
3. What happens if Suraj's normal speed is increased by a factor of 2?
4. How can we derive an equation for speed based on changing times?
5. How would the time difference be affected if the train's departure time changes?

**Tip:** In word problems like this, always start by expressing the unknown variables in terms of time, distance, and speed, and find relationships between them.

If Suraj travels at 8/9th of his usual speed, he misses a train by 10 minutes. But if he travels at 5/4th of his usual speed, he reaches the station 5 minutes before the departure of the train. What is the approximate normal time taken by Suraj to reach the railway station? A. 1 hour 4 minutes B. 52 minutes C. 37 minutes D. 46 minutes

Solve the time, speed, and distance problem where Suraj, traveling at different speeds, either misses the train or arrives early. Learn how to find the normal time taken using algebraic equations and the relationship between time, speed, and distance. Suitable for students in Grades 8-10.

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