Reiko's Trip - DS Question.

[RonPurewal]

Man, I was following you beautifully until the last line. How does s1= [40 (t1+t2)]/t1 go to 40+40(t2/t1) and then that ends in s1 > 40?

Thanks!

If you understand why (6x + 9y)/3 is equal to 2x + 3y, it's the same thing.

Yeahhhh, I see it now. Feel a bit foolish. Thanks

Small world by the way, I remember fondly taking your geometry class in high school :)

Small world indeed. Miami or Lafayette? Guessing the latter.

If I could sleep like a normal human being, I would almost definitely still be teaching high school. But that's another discussion for another place and time.

[camerons957]

Yeahhhh, I see it now. Feel a bit foolish. Thanks

Small world by the way, I remember fondly taking your geometry class in high school :)

Small world indeed. Miami or Lafayette? Guessing the latter.

If I could sleep like a normal human being, I would almost definitely still be teaching high school. But that's another discussion for another place and time.

Lafayette. Was many moons ago!

[tim]

If I could stay in one place like a normal human being, I would almost definitely still be teaching high school. :)

[QuinganZ341]

First off, make sure you are posting in the correct thread Manhattan CAT exam questions have their own forum section.

As for your question, the algebraic solutions for these types of questions are often difficult to understand, so in this case, let's come up with some very straightforward numbers to illustrate why statement (1) is sufficient. The statement talks about rates of 40 and 80 on a roundtrip, so I'm going to say that the distance from A to B is 40 miles and the roundtrip distance would be 80 miles.

If the entire trip is going to be finished at an average speed of 80mph, that means Reiko has less than 1 hour to get from A to B and back. If Reiko could travel back INSTANTLY from B back to A, then he could spend the entire hour traveling from A to B and cover 40 miles in 1 hour for a rate of 40mph. Since instant travel is not an available option on the GMAT, that means that Reiko would have had to spend less than an hour from A to B and traveled at a speed of greater than 40mph. Statement 1 is sufficient.

And as for your contention, remember to watch out for the question being asked. If Reiko did travel from A to B in instant time, he would have been speeding at a lot faster than 40mph.

The takeaway is that you can never double your average speed on the second leg of a roundtrip journey. Mathematically, this is because: r = d/t and to double your rate you would need to double the distance without adding any time: r = 2d/t.

Joe (or another moderator if Joe's no longer on staff) - could you please clarify the above explanation "If the entire trip is going to be finished at an average speed of 80mph, that means Reiko has less than 1 hour to get from A to B and back?"

I ask because (average rate)(total time) = total distance
thus, using the above numbers:
(80 miles/hour) (total time) = 80 miles
(total time) = 1 hour

You don't mean to say that total time is less than 1 hour, right?
You just mean to stay that since total time, which is t1 plus t2, = 1 hour, then t1 < 1 hour, and t2 < 1 hour, right?

And since d1 = 40 miles, and d2 = 40 miles, r1>40 miles/hour, and r2>40 miles/hour.

Thanks much in advance!

[tim]

Right. At 80 mph, the entire trip will take 1 hour, so EACH LEG will have to take less than an hour. Sorry for any confusion; it sounds like you understand what's going on.