Two cars A and B are running towards each other from two different places 88 km a part.If the ratio of the speeds of the cars A and B is 5:6 and the speed of the car B is 90km/h,after what time will they meet each other?

Options

A. 38 min
B. 39 min
C. 45 min
D. 32 min

Answer

To solve the problem step by step, we will follow the given information and apply the necessary calculations.

### Step 1: Understand the given information
- Two cars, A and B, are running towards each other from two places that are 88 km apart.
- The ratio of the speeds of cars A and B is 5:6.
- The speed of car B is given as 90 km/h.

### Step 2: Find the speed of car A
Since the ratio of the speeds of A and B is 5:6, we can express the speed of car A in terms of the speed of car B.

Let the speed of car A be \(5x\) and the speed of car B be \(6x\).
Given that the speed of car B is 90 km/h, we can set up the equation:
\[ 6x = 90 \]
To find \(x\), we divide both sides by 6:
\[ x = \frac{90}{6} = 15 \]

Now, we can find the speed of car A:
\[ \text{Speed of car A} = 5x = 5 \times 15 = 75 \text{ km/h} \]

### Step 3: Calculate the relative speed
Since cars A and B are moving towards each other, we can add their speeds to find the relative speed:
\[ \text{Relative speed} = \text{Speed of A} + \text{Speed of B} = 75 \text{ km/h} + 90 \text{ km/h} = 165 \text{ km/h} \]

### Step 4: Calculate the time taken to meet
We know the distance between the two cars is 88 km. To find the time taken for the cars to meet, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{88 \text{ km}}{165 \text{ km/h}} \]

### Step 5: Simplify the time calculation
To convert this into hours, we perform the division:
\[ \text{Time} = \frac{88}{165} \text{ hours} \]

To convert hours into minutes, we multiply by 60:
\[ \text{Time in minutes} = \frac{88}{165} \times 60 \]

### Step 6: Perform the multiplication and simplification
Calculating the multiplication:
\[ \text{Time in minutes} = \frac{88 \times 60}{165} \]
\[ = \frac{5280}{165} \]

Now we simplify \( \frac{5280}{165} \):
- Divide both the numerator and the denominator by 5:
\[ \frac{5280 \div 5}{165 \div 5} = \frac{1056}{33} \]

Now, we can simplify further:
- Divide both by 3:
\[ \frac{1056 \div 3}{33 \div 3} = \frac{352}{11} \]

Now, performing the division:
\[ 352 \div 11 = 32 \]

### Final Answer
Thus, the time taken for the two cars to meet is **32 minutes**.

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