A bulklock cart has to cover a distance of 80 km in 10 h. if It covers half of the journey in `3/5` th time , what should be its speed to cover the remaining distance in the left time

Options

A. a) 5 km/h
B. b)10 km/h
C. c)15 km/h
D. d) 18 km/h

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total distance and total time
The total distance to be covered is 80 km, and the total time allowed is 10 hours.

**Hint:** Always start by identifying the total distance and time given in the problem.

### Step 2: Calculate half of the journey
Half of the journey is \( \frac{80 \text{ km}}{2} = 40 \text{ km} \).

**Hint:** When a journey is divided into two equal parts, simply divide the total distance by 2.

### Step 3: Calculate the time taken for half of the journey
It is given that half of the journey is completed in \( \frac{3}{5} \) of the total time. So, we calculate the time taken for half the journey:
\[ \text{Time for half journey} = \frac{3}{5} \times 10 \text{ hours} = 6 \text{ hours} \]

**Hint:** To find a fraction of a total time, multiply the total time by the fraction.

### Step 4: Calculate the remaining time
The remaining time after completing half the journey is:
\[ \text{Remaining time} = 10 \text{ hours} - 6 \text{ hours} = 4 \text{ hours} \]

**Hint:** Subtract the time already spent from the total time to find the remaining time.

### Step 5: Determine the remaining distance
The remaining distance to be covered is also 40 km (since half of the journey is 40 km).

**Hint:** If the journey is symmetrical, the remaining distance will be equal to the distance already covered.

### Step 6: Calculate the speed required to cover the remaining distance
Speed is defined as distance divided by time. Therefore, the speed required to cover the remaining distance is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{40 \text{ km}}{4 \text{ hours}} = 10 \text{ km/h} \]

**Hint:** Remember the formula for speed: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

### Final Answer
The speed required to cover the remaining distance in the left time is **10 km/h**.

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