Answer:
Shop A is more expensive by $11.50 per hour
Step-by-step explanation:
I solved this three ways.
1) The difference in time for the two given charges is (6 -4) = 2 hours. The charge at Shop A for 2 hours is half the charge for 4 hours, so its equivalent rate for 6 hours is ...
Shop A rate for 6 hours = rate for 4 hours + rate for 2 hours
= $210 +105 = $315 . . . for 6 hours
This is way more than what Shop B charges for 6 hours.
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2) The difference in the charges is $246 -$210 = $36 for 2 hours difference in time. This is way less than the equivalent charge from Shop A for 2 hours, so the rate from Shop A is definitely higher.
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3) In order to answer the question, "how much more expensive?" we expect the rate difference will need to be expressed as a per-hour difference.* This means we have to figure the per-hour charge for each Shop and find the difference of them.
Shop A = $210/(4 h) = $52.50 /h
Shop B = $246/(6 h) = $41.00 /h
The rate from Shop A is higher by $52.50 -41.00 = $11.50 per hour.
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<em>Comments on How Much More</em>
* Using the first method, the rate difference is $315 -246 = $69 for 6 hours.
Using the second method, the rate difference is difficult to express exactly, but we can say the rate difference of $36 for 2 additional hours at Shop B is exceeded by the $105 expected charge for 2 additional hours at Shop A. That difference rate ($36/(2h)) isn't an actual charge anywhere, but represents a way to tell if the slope of one curve is more or less than the slope of the other.
If the rates were the same at the two shops, the charge at Shop B for 6 hours would be $315 as we figured in the first method, so the difference of $315 -210 = 105 would match exactly the increment at Shop A for 2 hours.
Personally, I see the second method as easiest to compute and most telling. However, to answer the question, "how much more expensive is it?", we needed to use one of the other methods.
