Two cars A and B are moving in same direction with a speed of 40km/h. the distance between cars A and B is constant and is 5km. Another car C is also moving in the same direction. If at a certain instant car B is overtaking C, then car A takes 20 minutes to overtake C. find speed of C?

Answer

To solve the problem step by step, we will analyze the motion of the cars involved and use the given information to find the speed of car C.

### Step 1: Understand the Given Information
- Cars A and B are moving in the same direction with a speed of 40 km/h.
- The distance between cars A and B is constant at 5 km.
- Car C is also moving in the same direction, and at a certain instant, car B is overtaking car C.
- Car A takes 20 minutes to overtake car C.

### Step 2: Convert Time from Minutes to Hours
Since speed is given in km/h, we need to convert the time taken to hours:
- Time taken by car A to overtake car C = 20 minutes = \( \frac{20}{60} \) hours = \( \frac{1}{3} \) hours.

### Step 3: Set Up the Relative Motion
When car A is overtaking car C, we can consider the relative speed of car A with respect to car C.
- Let the speed of car C be \( x \) km/h.
- The relative speed of car A with respect to car C is given by:
\[ \text{Relative Speed} = \text{Speed of A} - \text{Speed of C} = 40 - x \text{ km/h} \]

### Step 4: Use the Distance Formula
The distance that car A needs to cover to overtake car C is the distance between them, which is given as 5 km. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the known values:
\[ 5 \text{ km} = (40 - x) \text{ km/h} \times \frac{1}{3} \text{ hours} \]

### Step 5: Solve for \( x \)
Now, we can rearrange the equation to find \( x \):
\[ 5 = \frac{40 - x}{3} \]
Multiplying both sides by 3:
\[ 15 = 40 - x \]
Rearranging gives:
\[ x = 40 - 15 = 25 \text{ km/h} \]

### Conclusion
The speed of car C is \( 25 \) km/h.

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