MGRE Challenge: Orren's Commute

[MinorProphet]

Apologies if this is not the correct forum or if this issue has already been discussed elsewhere. I tried searching the forum before posting. I think there may be an error in the answer for the MGRE Challenge Problem Orren's Commute (Archived 2013, November 18). The correct answer is marked as "A". However, I think the correct answer should be "D". In the official solution they solved for the variable x, but the x they solved for is not necessarily the one in Quantity A. All you really know is that one of the speeds must be greater than 30 mph and the other must be less than 30 mph, you do not know which one is which.

The problem is pasted below for convenience. I'm not exactly sure how (or if I should) post the solution as it has several images. The images mostly show the algebraic steps involved in the solution.

EXERCISE:

Orren drove from his home to work in the morning at x miles per hour, and returned home in the evening at y miles per hour. His average speed for the round trip was 60 miles per hour.

Quantity A

x

Quantity B

30

[tommywallach]

Hey Orren,

The answer explains this, but I can try again.

The x is unknown, but that doesn't mean it can be anything. Let's imagine for a moment that Orren's trip is 120 miles. If his average speed for the round trip was 60 miles per hour, then the whole trip would take 4 hours.

Now let's imagine he drove at 30mph on the way there. That would take 4 hours, correct? But we wanted the WHOLE trip to take 4 hours (there and back). So 30mph is simply too slow if we want Orren to average 60mph.

Hope that makes sense.

-t

P.S. I've changed the title of your post and removed the "errata" word. In general, it's best to assume a problem with understanding, rather than an error in the book (though we've had plenty of errors, they are much more rare than problems of understanding). Thanks!