Ryan left the science museum and drove
south. Gabriella left three hours later
driving 42 km/h faster in an effort to catch
up to him. After two hours Gabriella finally
caught up. Find Ryan's average speed
since distance = speed * time, we need
x(3+2) = (x+42)(2)
x = 28
To find Ryan's average speed, we need to first determine the distance he covered during the two hours before Gabriella caught up to him.
Let's say Ryan's average speed is "x" km/h. During the two hours, he would have traveled a distance of 2x km.
Now, let's consider Gabriella's motion. She left three hours after Ryan and drove 42 km/h faster than him. So, her speed is (x + 42) km/h.
In the two hours it took Gabriella to catch up with Ryan, she covered a total distance of 2 * (x + 42) km.
Since Gabriella and Ryan were at the same location when she caught up, the total distance traveled by Ryan in his 2 hours and Gabriella in her 2 hours should be the same.
Therefore, we can set up the equation:
2x = 2 * (x + 42)
Simplifying the equation:
2x = 2x + 84
Subtracting 2x from both sides:
0 = 84
From the equation, we can see that 0 = 84, which is not possible. This suggests that there is no solution to the equation, and therefore, Ryan's average speed cannot be determined based on the given information.
It's important to note that there might be missing or inconsistent information in the problem statement, as it seems impossible to find the average speed of Ryan with the information provided.