Answer:
Step-by-step explanation:
Let's denote the time (in hours) it takes for the car to catch up with the truck as \(t\). The truck has been traveling for \(t+2\) hours when the car starts.
The distance traveled by the truck is given by the formula \( \text{Distance} = \text{Speed} \times \text{Time} \).
For the truck:
\[ \text{Distance}_{\text{truck}} = 35 \times (t + 2) \]
For the car:
\[ \text{Distance}_{\text{car}} = 56 \times t \]
When the car catches up with the truck, the distances traveled by both are equal. Therefore, we can set up an equation:
\[ 35 \times (t + 2) = 56 \times t \]
Now, solve for \(t\):
\[ 35t + 70 = 56t \]
\[ 21t = 70 \]
\[ t = \frac{70}{21} \]
\[ t = 3.\overline{333} \]
So, it takes approximately \(t \approx 3.\overline{333}\) hours for the car to catch up with the truck.
Now, add this time to the starting time of the car (which is 2 hours after the truck started) to find the total time:
\[ \text{Total time} = t + 2 \]
\[ \text{Total time} \approx 3.\overline{333} + 2 \]
\[ \text{Total time} \approx 5.\overline{333} \]
The car will catch up with the truck approximately 5.\overline{333} hours after 6:00 am. To find the time in a standard clock format:
\[ \text{Time} \approx 6:00 \, \text{am} + 5.\overline{333} \, \text{hours} \]
\[ \text{Time} \approx 11:20 \, \text{am} \]
So, the car will catch up with the truck at around 11:20 am.
