An aeroplane covers a distance at a 340 kmph in 8 hours. To cover the same distance in `2(2)/(3)` hours, it must travel at what speed ?

Options

A. 660 km/hr
B. 700 km/hr
C. 680 km/hr
D. 1020 km/hr

Explanation

To solve the problem step by step, we will first calculate the distance covered by the aeroplane and then determine the speed required to cover that same distance in a shorter time.

### Step 1: Calculate the distance covered by the aeroplane.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed = 340 km/h
- Time = 8 hours

Substituting the values into the formula:
\[ \text{Distance} = 340 \, \text{km/h} \times 8 \, \text{hours} \]
\[ \text{Distance} = 2720 \, \text{km} \]

### Step 2: Convert the time from mixed fraction to improper fraction.
The time given is \( 2 \frac{2}{3} \) hours. To convert this to an improper fraction:
\[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \, \text{hours} \]

### Step 3: Calculate the speed required to cover the same distance in \( \frac{8}{3} \) hours.
We will use the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting the values:
\[ \text{Speed} = \frac{2720 \, \text{km}}{\frac{8}{3} \, \text{hours}} \]

To divide by a fraction, we multiply by its reciprocal:
\[ \text{Speed} = 2720 \, \text{km} \times \frac{3}{8} \]

### Step 4: Perform the multiplication.
\[ \text{Speed} = \frac{2720 \times 3}{8} \]
\[ \text{Speed} = \frac{8160}{8} \]
\[ \text{Speed} = 1020 \, \text{km/h} \]

### Final Answer:
The aeroplane must travel at a speed of **1020 km/h** to cover the same distance in \( 2 \frac{2}{3} \) hours.

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