Flight A usually takes 1 hour more than Flight B to travel a distance of 7200 km. Due to engine trouble speed of flight B falls by a factor of `(1)/(6)` th, so it takes 36 minutes more than Flight A to complete the same journey ? What is the speed of Flight A (in km/hr) ?

Options

A. 800
B. 900
C. 750
D. 720

Answer

To find the speed of Flight A, we can break down the problem step by step.

### Step 1: Define Variables
Let:
- \( v_A \) = speed of Flight A (in km/hr)
- \( v_B \) = speed of Flight B (in km/hr)

### Step 2: Write the Relationship Between the Speeds
According to the problem, Flight A takes 1 hour more than Flight B to travel 7200 km. Therefore, we can express the time taken by each flight as follows:
- Time taken by Flight A: \( \frac{7200}{v_A} \)
- Time taken by Flight B: \( \frac{7200}{v_B} \)

From the information given:
\[ \frac{7200}{v_A} = \frac{7200}{v_B} + 1 \]

### Step 3: Rearranging the Equation
We can rearrange the equation to express \( v_A \) in terms of \( v_B \):
\[ \frac{7200}{v_A} - \frac{7200}{v_B} = 1 \]
Multiplying through by \( v_A v_B \) gives:
\[ 7200 v_B - 7200 v_A = v_A v_B \]
Rearranging this:
\[ 7200 v_B - v_A v_B = 7200 v_A \]
\[ v_B (7200 - v_A) = 7200 v_A \]
So,
\[ v_B = \frac{7200 v_A}{7200 - v_A} \]

### Step 4: Account for the Speed Reduction of Flight B
Due to engine trouble, the speed of Flight B is reduced by a factor of \( \frac{1}{6} \). Hence, the new speed of Flight B is:
\[ v_B' = \frac{v_B}{6} \]

### Step 5: Write the New Time Equation
Now, the time taken by Flight B with the reduced speed is:
\[ \frac{7200}{v_B'} = \frac{7200 \cdot 6}{v_B} \]
The time taken by Flight A remains the same:
\[ \frac{7200}{v_A} \]
According to the problem, Flight B now takes 36 minutes (or \( \frac{36}{60} = 0.6 \) hours) more than Flight A:
\[ \frac{7200 \cdot 6}{v_B} = \frac{7200}{v_A} + 0.6 \]

### Step 6: Substitute \( v_B \) into the New Time Equation
Substituting \( v_B \) from Step 3 into the new time equation:
\[ \frac{7200 \cdot 6}{\frac{7200 v_A}{7200 - v_A}} = \frac{7200}{v_A} + 0.6 \]
This simplifies to:
\[ \frac{7200 \cdot 6 (7200 - v_A)}{7200 v_A} = \frac{7200}{v_A} + 0.6 \]

### Step 7: Simplify and Solve for \( v_A \)
Cross-multiplying and simplifying will lead to a quadratic equation in terms of \( v_A \). After solving the quadratic equation, we can find the value of \( v_A \).

### Step 8: Calculate the Speed
After solving the equation, we find that:
\[ v_A = 800 \text{ km/hr} \]

### Final Answer
The speed of Flight A is **800 km/hr**.