A bike covers a certain distance at a speed of 56 km/hr in 16 hours. How much time it will take to cover the same distance at the speed of 64 km/hr?

Options

A. 14 hr
B. 18 hr
C. 16 hr
D. 12 hr

Answer

To solve the problem step by step, we will use the relationship between speed, time, and distance. The formula we will use is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 1: Calculate the Distance Covered
First, we need to find the distance covered by the bike during the first journey.

Given:
- Speed (S1) = 56 km/hr
- Time (T1) = 16 hours

Using the formula for distance:
\[ \text{Distance} = S1 \times T1 \]
\[ \text{Distance} = 56 \, \text{km/hr} \times 16 \, \text{hours} \]
\[ \text{Distance} = 896 \, \text{km} \]

### Step 2: Set Up the Equation for the Second Journey
Now, we need to find out how much time it will take to cover the same distance at a different speed (S2).

Given:
- Speed (S2) = 64 km/hr
- Distance = 896 km (from Step 1)

Using the formula for distance again, we can express the time (T2) for the second journey:
\[ \text{Distance} = S2 \times T2 \]
So,
\[ 896 = 64 \times T2 \]

### Step 3: Solve for Time (T2)
Now we will solve for T2:
\[ T2 = \frac{896}{64} \]

Calculating:
\[ T2 = 14 \, \text{hours} \]

### Conclusion
The bike will take 14 hours to cover the same distance at a speed of 64 km/hr.

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