Final answer:
By setting up an equation for the combined hourly earnings of the helper and mechanic, we calculate the helper's wage at $7 per hour and the mechanic's at $12 per hour. However, these results do not match any of the provided answer options, suggesting a possible error in the question or options.
Step-by-step explanation:
To solve this problem, we can set up an equation where x represents the hourly rate of the helper. Since the mechanic earns $5 more per hour than the helper, the mechanic's hourly rate would be x + $5. Together, on a six-hour job, they earn a total of $114.
The equation representing their combined earnings would be:
6x + 6(x + $5) = $114
Distributing the 6 into the parentheses gives us:
6x + 6x + $30 = $114
Combining like terms, we get:
12x + $30 = $114
Subtracting $30 from both sides gives:
12x = $84
Dividing both sides by 12, we find that:
x = $7. Therefore, the helper earns $7 per hour. The mechanic earns $7 + $5 = $12 per hour.
However, since none of the provided answer options match our calculations, it's possible there was a mistake in the question or in the provided options. It's important to double-check the question and the options to ensure accuracy.