Manpreet took part in an interschool race competition He cylcled 2.7 km, ran for `(2)/(3)` hour and walked the remaining 500 m of the race. If the total distance of the race was 12 km, then find his running speed

Options

A. 13.2 km/hr
B. 12 km/hr
C. 7.5 km/hr
D. 8.8 km/hr

Answer

To find Manpreet's running speed, we can follow these steps:

### Step 1: Determine the total distance of the race
The total distance of the race is given as 12 km.

### Step 2: Calculate the distance cycled and walked
Manpreet cycled 2.7 km and walked 500 m. First, we need to convert the distance walked into kilometers:
- 500 m = 500/1000 km = 0.5 km

### Step 3: Calculate the total distance cycled and walked
Now, we add the distance cycled and the distance walked:
- Distance cycled = 2.7 km
- Distance walked = 0.5 km
- Total distance cycled and walked = 2.7 km + 0.5 km = 3.2 km

### Step 4: Calculate the distance run
To find the distance run, we subtract the total distance cycled and walked from the total distance of the race:
- Distance run = Total distance - Distance cycled and walked
- Distance run = 12 km - 3.2 km = 8.8 km

### Step 5: Determine the time spent running
The time spent running is given as \( \frac{2}{3} \) hour.

### Step 6: Calculate the running speed
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values we have:
\[ \text{Speed} = \frac{8.8 \text{ km}}{\frac{2}{3} \text{ hour}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Speed} = 8.8 \text{ km} \times \frac{3}{2} \]
Calculating this gives:
\[ \text{Speed} = \frac{8.8 \times 3}{2} = \frac{26.4}{2} = 13.2 \text{ km/h} \]

### Final Answer
Manpreet's running speed is **13.2 km/h**.

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