Final answer:
To determine John's driving speed in the morning, we need to use the formula distance = speed x time. We can set up equations based on the distance he traveled in the morning and after lunch. However, additional information is needed to solve the problem.
Step-by-step explanation:
To determine how fast John drove in the morning, we need to first find out the distance he traveled and the time he spent driving before lunch. We know that he completed a 490-mile trip in 9 hours of driving time. Let's assume he drove x hours in the morning and (9 - x) hours after lunch.
In the morning, he drove at a certain speed. After lunch, he increased his speed by 10 mph. Let's say his morning speed was s mph. Therefore, his afternoon speed would be (s + 10) mph.
Using the formula distance = speed x time, we can set up two equations:
- Distance driven in the morning: x hours * s mph = x * s miles
- Distance driven after lunch: (9 - x) hours * (s + 10) mph = (9 - x) * (s + 10) miles
Since the total distance driven is 490 miles, we can write the following equation:
x * s + (9 - x) * (s + 10) = 490
Simplifying the equation, we get:
x * s + 9s + 90 - xs - 10x = 490
Combining like terms, we have:
10s - x + 90 = 490
Subtracting 90 from both sides, we get:
10s - x = 400
Now we need additional information to solve for x and s. Could you provide any other details or numbers given in the problem?