Find the ratio of :
5 hours and 50 minutes to 8 hours and 10 minutes.

Answer

To find the ratio of 5 hours and 50 minutes to 8 hours and 10 minutes, we can follow these steps:

### Step 1: Convert hours and minutes to minutes
First, we need to convert both times into minutes.

- For 5 hours and 50 minutes:
\[ 5 \text{ hours} = 5 \times 60 = 300 \text{ minutes} \]
Adding the 50 minutes:
\[ 300 + 50 = 350 \text{ minutes} \]

- For 8 hours and 10 minutes:
\[ 8 \text{ hours} = 8 \times 60 = 480 \text{ minutes} \]
Adding the 10 minutes:
\[ 480 + 10 = 490 \text{ minutes} \]

### Step 2: Write the ratio
Now we can write the ratio of the two times in minutes:
\[ \text{Ratio} = \frac{350 \text{ minutes}}{490 \text{ minutes}} \]

### Step 3: Simplify the ratio
Next, we simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 350 and 490 is 70. So we divide both by 70:
\[ \frac{350 \div 70}{490 \div 70} = \frac{5}{7} \]

### Step 4: Write the final answer
Thus, the ratio of 5 hours and 50 minutes to 8 hours and 10 minutes is:
\[ \text{Ratio} = 5 : 7 \]

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