Maggie commutes to work by train at a rate of 62 mph and then by car at a rate of 46 mph. How long will it take her to travel the 54 miles to work if she is on the train and in the car for equal periods of time? I just want to make sure I've set it up right: 62(x)+46(54-x)=54 ?

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Maggie commutes to work by train at a rate of 62 mph and then by car at a rate of 46 mph. How long will it take her to travel the 54 miles to work if she is on the train and in the car for equal periods of time? I just want to make sure I've set it up right: 62(x)+46(54-x)=54 ?

Mathematics
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I think you are close, but let me double check. I'm not totally sure on the 54-x part.
If it makes any difference I just corrected the wrong parenthesis between 46 and 54.
Accidentally did a ) when I meant an (...

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Ah... I see! No worries.
Alright, so there's a minor problem with your equation. But let's start with what you have so far. What are you thinking that the x means in your equation?
x is the amount of time for the first person. So then once we find that out, the second person's time is the total minus the first person's. Although I might be getting concepts from various types of problems discussed in the lessons mixed up.
No worries. That's a good explanation of what you are thinking right now. It's perfectly fine and normal in math to be wrong. The important thing is clearly understanding what you are thinking.
So, the first thing I notice is that in your explanation you mention "two" people. But our problem only has one person - Maggie.
I'm guessing that what you mean to say is: x is the amount of time ON THE TRAIN. Then the amount of time IN THE CAR is the total minus the time on the train.
Yes sorry that was a mistake... I was just doing a problem that was that. So yes, train and car is what I meant.
Alright, perfect! We are both on the same page. :)
Now, notice though that they gave you an extra hint "she is on the train and in the car for equal periods of time" We don't even need to take the total and minus the time on the train. The time on the train is x, and the time in the car is equal (also x). Make sense so far?
Yes, I just don't know how to make that equation then.
No worries. Your first equation that you wrote was very, very close. :) The distance traveled is given by d = rt right? So, Distance on the train = 62x Distance in the car = 46x
*set up that equation, to make that sound better.
Okay.
We know these distances add up to a total of 54 from the question. So, 62x + 46x = 54
Only difference from your original is that we don't have (54 - x), we just have x. That's based on the extra hint they gave us.
It's actually an easier equation to solve. Does that make sense so far? Where would you go from here? :)
Okay! Thank you! I was just overcomplicating this!
Next I would combine 62x and 46x to make 108x, then divide 54 by 108, correct?
Good! And then what do you get?
0.53 is close enough since I only have to round to the nearest tenth! Thank you so much!
There's just one more little trick that they might try to pull with the question. We are fine so far. But once you find x, that is NOT the answer they want. They want the total time, which is the time on the train + the time in the car or x + x or 2x is the real answer.
If I'm not mistaken 54/108 is actually 0.5 exactly so no rounding required. :)
And I do or don't have to multiply that by two then? Also sorry I must have made a mistake in the division. Sorry, I've been doing math all day so I'm a little burned out.
Not a problem, you are doing great!
OK, so we had 108x = 54, then x = 0.5 x is the time on the train (or the time in the car). We need the total time, and 0.5 is just the time on the train. So, we DO multiply by 2 to get Total time is 1 hr. Tricky fish! :)
Thank you! But I have a small problem... The multiple choice answers are 2 hours 0.5 hours 3.4 hours 0.3 hours
Interesting... let me check our calculations to ensure we didn't do anything silly. :)
Hmm... I don't think we made any mistakes... If I HAD to pick an answer, 0.5 hours makes the most sense... but that's just a hunch.
Something seems wrong with the answer choices.
For the record, it is possible for it to be a mistake in the school system. It's happened before, although it's rare on this system.
Alright! Thank you so much! Hopefully after this help I won't have to come back here too much more tonight, but we'll see!
Good luck! Your welcome, hope you get credit for the thinking! :)

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