In covering a certain distance, the speed of A and B are in the ratio of `3:4`. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is

Options

A. 1 hour
B. `1 (1)/(2)` hours
C. 2 hours
D. `2(1)/(2)` hours

Answer

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

### Step 1: Understand the speed ratio
The speeds of A and B are given in the ratio of 3:4. This means if the speed of A is 3x, then the speed of B is 4x, where x is a common multiplier.

**Hint:** Remember that when speeds are in a ratio, the time taken is inversely proportional to the speed.

### Step 2: Determine the time ratio
Since speed and time are inversely related, the time taken by A and B will be in the ratio of the inverse of their speeds. Therefore, the time ratio of A to B will be 4:3.

**Hint:** Inverse the speed ratio to find the time ratio.

### Step 3: Define the time taken
Let the time taken by B to reach the destination be 3y minutes. Then, the time taken by A will be 4y minutes.

**Hint:** Use a variable (y) to represent the time taken by B and express A's time in terms of y.

### Step 4: Set up the equation
According to the problem, A takes 30 minutes more than B. Therefore, we can set up the equation:
\[ 4y = 3y + 30 \]

**Hint:** Set up an equation based on the information given about the time difference.

### Step 5: Solve the equation
Now, solve for y:
\[ 4y - 3y = 30 \]
\[ y = 30 \]

**Hint:** Isolate y to find its value.

### Step 6: Calculate the time taken by A
Now that we have y, we can find the time taken by A:
\[ \text{Time taken by A} = 4y = 4 \times 30 = 120 \text{ minutes} \]

**Hint:** Substitute the value of y back into the equation for A's time.

### Step 7: Convert minutes to hours (if necessary)
120 minutes can be converted to hours:
\[ 120 \text{ minutes} = 2 \text{ hours} \]

**Hint:** Remember that 60 minutes equals 1 hour.

### Final Answer
The time taken by A to reach the destination is **120 minutes** or **2 hours**.

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