A bus travels 700 km at a certain speed. If the bus driver reduces the speed of bus to 20 km/h then the bus will take four hours more to travel the same distance. Then find the initial speed of the bus ?

Answer

To solve the problem step by step, let's denote the initial speed of the bus as \( x \) km/h.

### Step 1: Write the equation for time taken at initial speed
The time taken to travel 700 km at the initial speed \( x \) is given by:
\[ T_1 = \frac{700}{x} \]

### Step 2: Write the equation for time taken at reduced speed
When the speed is reduced to 20 km/h, the time taken to travel the same distance is:
\[ T_2 = \frac{700}{20} = 35 \text{ hours} \]

### Step 3: Set up the equation based on the information given
According to the problem, the time taken at the reduced speed is 4 hours more than the time taken at the initial speed. Therefore, we can write:
\[ T_2 = T_1 + 4 \]
Substituting the expressions for \( T_1 \) and \( T_2 \):
\[ 35 = \frac{700}{x} + 4 \]

### Step 4: Solve for \( x \)
Now, we will solve the equation for \( x \):
\[ 35 - 4 = \frac{700}{x} \]
\[ 31 = \frac{700}{x} \]
Cross-multiplying gives:
\[ 31x = 700 \]
Now, divide both sides by 31:
\[ x = \frac{700}{31} \approx 22.58 \text{ km/h} \]

### Step 5: Conclusion
Thus, the initial speed of the bus is approximately \( 22.58 \) km/h.