Running at 5/4 of his usual speed, an athlete improves his liming by 5 minutes. The time he usually takes to run the same distance is:

Options

A. 30 min.
B. 28 min.
C. 25 min.
D. 23 min.

Answer

To solve the problem step by step, let's denote the usual time taken by the athlete to run a certain distance as \( T \) minutes.

### Step 1: Define the usual speed and the new speed
Let the usual speed of the athlete be \( S \). When the athlete runs at \( \frac{5}{4}S \), this is the new speed.

### Step 2: Relate speed and time
We know that speed is inversely proportional to time for a constant distance. Therefore, if the speed increases, the time taken will decrease. The new time taken \( T' \) can be expressed as:
\[ T' = \frac{D}{\frac{5}{4}S} = \frac{4D}{5S} \]
Since distance \( D \) is constant, we can relate the times directly:
\[ T' = \frac{4}{5}T \]

### Step 3: Set up the equation based on the time saved
According to the problem, the athlete improves his timing by 5 minutes. Therefore, we can set up the equation:
\[ T - T' = 5 \]
Substituting \( T' \) from the previous step:
\[ T - \frac{4}{5}T = 5 \]

### Step 4: Simplify the equation
Now, simplify the left side of the equation:
\[ \frac{1}{5}T = 5 \]

### Step 5: Solve for \( T \)
To find \( T \), multiply both sides by 5:
\[ T = 25 \]

### Conclusion
The time the athlete usually takes to run the same distance is **25 minutes**.

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