Well it depends on what chemistry. But if we assume its a lithium chemistry since that’s what modern electric cars usually use:
The charging profile time vs capacity is not linear well before 100%. Although I think this is for LiPo’s not LiFePo4’s which is what I think cars usually use. Couldn’t find a comparable chart for LiFePo4’s.
I love this board. Who’d’ve thought* that such a simple question about a cartoon would move into this discussion of mathematics and physics?
*I mean who, besides someone who’s been on this site more than ten seconds.
Particularly for younger kids, where they’re not trying to play “gotcha” games, they’re trying to teach basic math. Were I to give the same question to University students, I might expect a lecture about the unstated assumptions.
Yes, they’re trying to teach basic math.
But the kids still need to translate the words into (unrealistically simple) formulas to do that math. If their text-to-formula conversion is full of unstated and probably unrecognized guesswork, the problem probably has negative learning value.
Because the real point is not to learn to multiply or divide 85% by 30 by 40, but to figure out which combination of operations on which operands solves the stated problem. If the book/teacher just wanted arithmetic drills, why introduce all the words and attendant opportunities for confusion?
In this specific case the critical missing quantity is the starting level of charge. Absent that the question amounts to “Alice has a 5 gallon bucket with (maybe) some water already in it. Adding water at 3 gallons per minute, how long will it take for her bucket to overflow?”
If the kids are to the point already of learning & understanding less than / greater than relationships, they can rightly answer my bucket question as “At most 5/3 minutes.” If they’re still back at computing only equalities then the question as posed is unanswerable.
I’m still shitty about my older son being marked down on a mechanics/math problem because he answered on the assumption there would be friction. But apparently I’m wrong according to the teachers, my math teacher father and my mathematics Olympiad brother. Apparently my son should have realised they were looking for the simpler answer not including friction.
I’m not bitter at all.
I’ve always said “You cannot be smarter than the person who wrote the test and still get a good score.”
As somebody who was (or thought he was) smarter than the vast majority of test writers for kids’ tests, this was the bane of my small existence. Arguing with an authority figure who’s 2-3 feet taller than you are also never works. I learned that too at an early age. “Someday you’ll all Pay for this Outrage!!” [shakes little fist at eye-rolling Mrs. Jones.]
Sorry your son had to have the same experience, but it’s pretty universal. 
At least among the brightest kids which yours undoubtedly were / are. 
Flattery will get you everywhere.
That level of charging is very efficient. My last charge, plugged into a 240V 30A outlet, was rated at 97% efficiency. Also, at only 5.8kW (see below), the charging speed is going to be linear up to 98% or so. It should run at full speed from whatever level it starts at to 85%
This is another “missing assumption” in the problem. A 240V 30A circuit is only going to provide 24A of continuous current. If “source” means something connected to a 30A breaker, then the actual charging rate is 5.8kW.
If the source really is providing 30A continuous power, then that it a bit strange. The next common step up would be a 50A circuit, which can provide 40A continuous. The likely explanation is a 50/40A source, but the cars internal AC to DC converter is only capable of doing 30A, so the battery is only being charged at 7.2kW, even though the circuit is capable of providing 9.6kW.
Also, what’s the voltage drop at the supply when pulling that much power? What if the AC in the house comes on? That could add minutes to the charging time!
How is this calculated? Is this due to the conversion from AC to DC or something else.
8 or 9 seems a bit young, but this seems like a plausible (maybe stretch goal) grade school math problem.
You have to be able to multiply 40 by .85, 240 by 30, divide one of the results by the other, and understand that volts x amps = watts and the SI “k” prefix means multiply or divide by 1000 somewhere. Pretty sure I learned all that stuff by 6th grade.
I could see this showing up earlier than HS because “how long will it take to charge an electric car” is an increasingly relevant real-life math problem.
The amps given for a circuit are the peak load, and the continuous load is 80% of peak. So a 15A breaker is rated for 12A continuous, 20A = 16A, etc. Somebody who knows more about it might come along to explain any exceptions, or what exactly is meant by “continuous”. Charging a car for three+ hours is definitely a continuous load.
If you have a 30A breaker and are drawing 30A then… if there’s a minor fluctuation of voltage or current, the breaker will (if doing it’s job) pop. It’s like filling a cup to the rim. there’s no room for give. The 80% rule is strongly recommended for all loads as a safety margin. Exceed it at your peril.
A Tesla 3 RWD will AFAIK charge at 32A (240V) while a model 3 AWD will charge at a maximum of 40A. The portable charger is limited to 32A.
I have 100A service, and a 50A breaker so charge my Tesla at 40A. However, once in the middle of the night, my main breaker went off. (I figure the AC and hot water tank may have kicked in too about then… freezer too?) So I’ve dialed the car back to only charge 26A. It starts at 1AM. No problems. Other cars could have different rates.
I definitely thought of Jason Fox when I saw that - and even if it isn’t a real math problem, he and Marcus probably could figure out how to solve it.
Are we also assuming that she’s starting with 0% charge on the battery? Or is she starting at 85% and shooting for 100%?
No, it’s not a legitimate math problem, because legitimate math problems don’t permit unstated assumptions.
Sonia can probably look up the charging rates in the vehicle’s owner manual.
The problem in the strip said, “…to 85%”, so I’d have to say that’s the target value.
Bill Amend has a degree in Physics, so it’s not too surprising.
Yet they do, nonetheless.
I mean, I suppose it’s conceivable that the manual would have something that useful.
But once again, either you or the problem are making assumptions. The problem says it’s a 30 amp source. Not a 30 amp circuit, or 30 amp breaker. So maybe the 20% margin is already built into the 30 amp figure.
Really, it tends to depend on what the class has been taught. If they’ve been taught that every source can only be used at 80% then I suppose for full marks they would be expected to know to down rate the 30 amps to 24. But if not, it would outrageous to expect a schoolkid to know about this issue.
Math problems regularly have unstated assumptions, just like real life does, and most of the objections in this thread are very silly.
The purpose of word problems is to teach children to find the necessary information, discard unnecessary information, and to convert English (which is generally not a mathematically precise language) into a mathematical expression that can be evaluated.
We don’t need to care about the efficiency of the charger or the starting charge or the circuit breaker capacity or how far away Grandma’s house is, because none of those are part of the problem.
This problem tests knowledge of multiplication, division, percentages, and dimensional analysis of time and electric potential, current, and energy, and it’s a perfectly fine word problem for someone who knows those things.
Here’s another word problem: “Jim is at a baseball game with his parents and two sisters. If hot dogs cost $3 each and sodas cost $1, how much money does Jim need to buy food and drinks for himself and his family if each person gets a drink, each child eats one hot dog and each adult eats two?”
This problem has one correct and obvious answer, but if you’re an insufferable pedant, you could point out the ways in which it is underspecified because English is a natural language. You would be missing the point.
For example, here are some ways to miss the point: “We can’t answer because we don’t know how much money Jim already has, and the question asks how much he needs.”, “The problem doesn’t tell us what the tax rate is”, or “The problem doesn’t specify ages; maybe Jim and/or some of his sisters are legal adults and will eat two hot dogs each”.
Stop being ridiculous.