Final answer:
Bryce was traveling at 21 mph, and Sydney was traveling at 31 mph, with Bryce's speed determined by solving the equation 3x + 3(x + 10) = 156, where x is Bryce's speed in mph.
Step-by-step explanation:
Bryce and Sydney are 156 miles apart and are traveling towards each other. Sydney travels 10 mph faster than Bryce and they meet after 3 hours. To determine how fast each was traveling, let's define Bryce's speed as x mph and Sydney's as x + 10 mph. Since they meet after 3 hours, the combined distance they cover will equal 156 miles. The equation to represent this situation is:
3x + 3(x + 10) = 156
Solving for x, we add the terms involving x:
3x + 3x + 30 = 156
Combine like terms:
6x + 30 = 156
Subtract 30 from both sides:
6x = 126
Divide by 6:
x = 21
Now we know Bryce was traveling at 21 mph and Sydney was traveling at 31 mph since she was moving 10 mph faster than Bryce.