RTD style question

[ErikM442]

I found a question through Khan Academy where the question goes as follows:

A jogger and a walker set out at 9am from the same point, headed in the same direction. The average speed of the jogger is 1 mph slower than twice the speed of the walker. In two hours, the jogger is 3 miles ahead of the walker. Find the rate of the jogger.

How would you go about putting this in an RTD chart? I can't seem to figure it out.

Thanks in advance.

[RonPurewal]

well, first set it up the usual way, with rows labeled "walker" and "jogger" (or W and J, or whatever).

also, i don't personally recommend "R", "T", and "D"--at least not by themselves. instead, you should label the columns with units (mi/hr, hr, mi).
there are at least two advantages here:
1/ you'll be able to use the chart more quickly, because the meaning of the columns will be more obvious;
2/ if there's any monkey business with units--e.g., speeds in miles per hour but times in minutes--you won't let it slip past you.

--

so, assuming your rows are mi/hr.....hr.....mi, use this:

The average speed of the jogger is 1 mph slower than twice the speed of the walker.

walker: x........2...[blank]
jogger: 2x-1....2...[blank]

then you can fill in the blanks (with 2x and 4x - 2, respectively). at this point the only remaining fact is the "3 miles ahead" thing. so, 4x - 2 is three more than 2x. then solve from there.

[RonPurewal]

you can also think about the difference between the speeds:
• they run for the same amount of time
• ...but the jogger goes 3 more miles
so, we know that, at these speeds, the jogger goes 3 more miles every 2 hours.
in other words, the jogger's speed is 1.5 mi/hr faster than the walker's.

at this point, you have two equations, j = w + 1.5 and (from the problem statement) j = 2w - 1. the solution from there is routine.

[RonPurewal]

...and, lastly, if there are answer choices (as there certainly would be on this exam), you can just backsolve.

let's say an answer choice says "jogger goes 4 mi/hr".
ok.
in that case, 4 = 2(walker's speed) - 1, so walker's speed would be 2.5 mi/hr.

then, just check how far they go in 2 hours.
jogger: 4 x 2 = 8 miles
walker: 2.5 x 2 = 5 miles
this is the required three-mile difference, so we're done. (any wrong answer would give a difference of ... not three miles.)

[RonPurewal]

it's also worth noting that the answer to this problem is not very realistic in the real world, where both 2.5 mi/hr (a slow stroll, maybe even the walk of someone who's rehabilitating an injured knee) and 4 mi/hr (a brisk walk) are both walking speeds. no jogger is going to jog 15-minute miles!

this is significant because GMAC's answers are always sensible--and unremarkable--in the real world. if you had a "jogger" on the gmat, that person would be going at least, say, 5 mi/hr.