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 ?

- Republican31

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- jtvatsim

I think you are close, but let me double check. I'm not totally sure on the 54-x part.

- Republican31

If it makes any difference I just corrected the wrong parenthesis between 46 and 54.

- Republican31

Accidentally did a ) when I meant an (...

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- jtvatsim

Ah... I see! No worries.

- jtvatsim

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?

- Republican31

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.

- jtvatsim

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.

- jtvatsim

So, the first thing I notice is that in your explanation you mention "two" people. But our problem only has one person - Maggie.

- jtvatsim

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.

- Republican31

Yes sorry that was a mistake... I was just doing a problem that was that. So yes, train and car is what I meant.

- jtvatsim

Alright, perfect! We are both on the same page. :)

- jtvatsim

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?

- Republican31

Yes, I just don't know how to make that equation then.

- jtvatsim

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

- Republican31

*set up that equation, to make that sound better.

- Republican31

Okay.

- jtvatsim

We know these distances add up to a total of 54 from the question. So,
62x + 46x = 54

- jtvatsim

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.

- jtvatsim

It's actually an easier equation to solve. Does that make sense so far? Where would you go from here? :)

- Republican31

Okay! Thank you! I was just overcomplicating this!

- Republican31

Next I would combine 62x and 46x to make 108x, then divide 54 by 108, correct?

- jtvatsim

Good! And then what do you get?

- Republican31

0.53 is close enough since I only have to round to the nearest tenth! Thank you so much!

- jtvatsim

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.

- jtvatsim

If I'm not mistaken 54/108 is actually 0.5 exactly so no rounding required. :)

- Republican31

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.

- jtvatsim

Not a problem, you are doing great!

- jtvatsim

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! :)

- Republican31

Thank you! But I have a small problem... The multiple choice answers are
2 hours
0.5 hours
3.4 hours
0.3 hours

- jtvatsim

Interesting... let me check our calculations to ensure we didn't do anything silly. :)

- jtvatsim

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.

- jtvatsim

Something seems wrong with the answer choices.

- Republican31

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.

- Republican31

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!

- jtvatsim

Good luck! Your welcome, hope you get credit for the thinking! :)

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