Walking at 4/5 of his original speed, a man reaches his destination by 5 minutes late. Find his original time

Questions : Walking at 4/5 of his original speed, a man reaches his destination by 5 minutes late. Find his original time.

Answer:  

 Using the shortcut formula:

$$T = \frac{\text{Late Time}}{\left(\frac{\text{Reduced Speed}}{\text{Original Speed}} - 1\right)}$$

Given:

• Reduced speed = $\frac{4}{5}$ of original speed
• Late time = 5 minutes

Applying the formula:

$$T = \frac{5}{\left(\frac{4}{5} - 1\right)}$$ $$T = \frac{5}{\left(\frac{4}{5} - \frac{5}{5}\right)}$$ $$T = \frac{5}{\left(-\frac{1}{5}\right)}$$ $$T = 5 \times 5 = 25 \text{ minutes}$$

Final Answer:

The man's original time was 25 minutes.

Additional Information

Here's how to solve this problem:

1. Understand the Relationship

Speed and time are inversely proportional when the distance is constant. This means that if the speed decreases, the time taken increases, and vice versa.

2. Set up the Equation

Let 't' be the original time taken in minutes.

• Original speed: Let's call it 's'.
• Original time: t minutes
• New speed: (4/5)s
• New time: t + 5 minutes

Since the distance is the same in both cases:

Original speed * Original time = New speed * New time

s * t = (4/5)s * (t + 5)

3. Solve for t

1. Cancel 's' from both sides:

   t = (4/5)(t + 5)

2. Distribute the (4/5):

   t = (4/5)t + (20/5)

3. Simplify the fraction:

   t = (4/5)t + 4

4. Subtract (4/5)t from both sides:

   t - (4/5)t = 4

5. Find a common denominator and subtract:

   (1/5)t = 4

6. Multiply both sides by 5:

   t = 20

Answer:

The man's original time to reach his destination was 20 minutes.

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