Answer:
- equation: 16x = 18 +12x
- solution to the equation: x = 4 1/2 hours
- solution to the problem: 2 5/8 hours
Step-by-step explanation:
The relevant relation is ...
distance = speed × time
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If we use x to represent hours after Wanda starts the race, the distance she travels at 16 miles per hour is ...
16x . . . . miles
Hector has already traveled 18 miles. The distance he travels in x hours after Wanda starts the race is 12x at 12 miles per hour. His total distance from the start of the race is ...
18 +12x . . . . miles
Wanda will catch up to Hector when these two distances are equal. That is the equation you want to write:
16x = 18 +12x
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To solve this equation, you subtract 12x from both sides.
16x -12x = 18 +12x -12x
4x = 18
Then, you divide both sides by 4.
4x/4 = 18/4
x = 9/2 = 4 1/2
If the given rates are maintained, Wanda will catch up to Hector after she rides 4 1/2 hours.
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Additional comment
It should be noted here, that Hector will finish his remaining 42 -18 = 24 miles in (24 mi)/(12 mi/h) = 2 hours. Wanda will catch Hector at the finish line when she gets there after (42 mi)/(16 mi/h) = 2 5/8 hours, assuming Hector is still waiting.
You may want to discuss this question with your teacher to see if you are supposed to consider the practical domain of the equation you found.
