Respuesta :
Answer:
Please check your answer for the same
Step-by-step explanation:
To find out how much time it will take for the two cars to meet, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Since they are driving towards each other, their combined speed will be the sum of their individual speeds.
Let's denote:
- \( d \) as the distance between the two cars (initially 200 km)
- \( v_1 \) as the speed of the first car (40 km/hr)
- \( v_2 \) as the speed of the second car (100 km/hr)
We need to find out when the sum of the distances covered by both cars equals the initial distance between them, \( d = 200 \) km.
At time \( t \), the distance covered by the first car is \( v_1 \times t \), and the distance covered by the second car is \( v_2 \times t \).
Using the formula, we can set up the equation:
\[ d = v_1 \times t + v_2 \times t \]
\[ 200 = (40 + 100) \times t \]
\[ 200 = 140 \times t \]
\[ t = \frac{200}{140} \]
\[ t = \frac{20}{14} \]
\[ t = \frac{10}{7} \]
Therefore, it will take \( \frac{10}{7} \) hours for the two cars to meet. To convert this to minutes:
\[ \frac{10}{7} \times 60 = \frac{600}{7} \approx 85.71 \text{ minutes} \]
So, it will take approximately \( 85.71 \) minutes for the two cars to meet.
