A and B travel the same distance at 9 km/h and 10 km/h respectively.if A takes 20 minutes longer than B the distance travelled by each is:

Options

A. 16
B. 20
C. 30
D. none of these

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the variables
Let the distance traveled by both A and B be \( D \) kilometers.

### Step 2: Write the speeds
- Speed of A = 9 km/h
- Speed of B = 10 km/h

### Step 3: Write the time taken by A and B
The time taken by A to travel distance \( D \) is given by:
\[ \text{Time taken by A} = \frac{D}{9} \text{ hours} \]
The time taken by B to travel the same distance \( D \) is given by:
\[ \text{Time taken by B} = \frac{D}{10} \text{ hours} \]

### Step 4: Set up the equation based on the time difference
According to the problem, A takes 20 minutes longer than B. We need to convert 20 minutes into hours:
\[ 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \]
So, we can set up the equation:
\[ \frac{D}{9} = \frac{D}{10} + \frac{1}{3} \]

### Step 5: Solve the equation
To eliminate the fractions, we can multiply through by the least common multiple of the denominators (90):
\[ 90 \left(\frac{D}{9}\right) = 90 \left(\frac{D}{10}\right) + 90 \left(\frac{1}{3}\right) \]
This simplifies to:
\[ 10D = 9D + 30 \]
Now, subtract \( 9D \) from both sides:
\[ 10D - 9D = 30 \]
\[ D = 30 \]

### Step 6: Conclusion
The distance traveled by each A and B is \( 30 \) kilometers.

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