A person covers a certain distance by travelling at a uniform speed of 120 km per hour for 90 minutes. At what speed will he have to travel in order to cover the same distance in 1 hour 20 minutes? ( in km per hour)

Options

A. 135
B. 125
C. 140
D. 130

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the distance covered at the initial speed.
- The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Given speed = 120 km/h and time = 90 minutes. First, we need to convert 90 minutes into hours:
\[ 90 \text{ minutes} = \frac{90}{60} \text{ hours} = 1.5 \text{ hours} \]
- Now, substituting the values into the distance formula:
\[ \text{Distance} = 120 \text{ km/h} \times 1.5 \text{ hours} = 180 \text{ km} \]

### Step 2: Convert the second time duration into hours.
- The second time duration is 1 hour and 20 minutes. We convert this into hours:
\[ 1 \text{ hour} + 20 \text{ minutes} = 1 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3} \text{ hours} \]

### Step 3: Calculate the speed required to cover the same distance in the new time.
- We will use the distance formula again, rearranging it to find speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- We already calculated the distance as 180 km. Now substituting the values:
\[ \text{Speed} = \frac{180 \text{ km}}{\frac{4}{3} \text{ hours}} = 180 \times \frac{3}{4} = 135 \text{ km/h} \]

### Conclusion:
The speed required to cover the same distance in 1 hour and 20 minutes is **135 km/h**.

---