Guide 4 (4th edition), Advanced Rate and Work Problems

[anguyen2107]

This question pertains to sample problem about Liam's actual and hypothetical rate: Chapter 11, p. 171.

Although i understand the explanation upon close examination, the thinking behind the rate and time relationships described in the RTD chart is not as intuitive as my way of approaching the problem. I got the same answer by setting up the RTD chart (relationships) differently. Please confirm that the alternate approach is equally valid.

Original (see text for rationale):

_______Rate___X___Time___ =___Distance
Actual__r + 5____30/(r +5)_______ 30
Hyp_____r ________30/r _________30

equation set-up, 30/r = 30/ (r + 5) + 1/15

Alternate set-up: the way i had translated the word problem is more literal to the question stem, while the original, text-book version had a slight inversion of thinking. Since the hypothetical rate was 5 miles less than the actual rate, i made the actual rate r, and the Hyp rate r-5. Similarly, since Liam arrived 4 minutes earlier under the actual rate, i subtracted 1/15 minutes from the hypo time (see equation).

_______Rate___X___Time___ =___Distance
Actual___r__________30/r_________ 30
Hyp____r - 5 ______30/(r-5)________30

equation set-up, 30/r = 30/ (r - 5) - 1/15


* Please confirm that my way of thinking will also conclusively arrive at the right answer every time for this type of problem.

[Ben Ku]

Your approach is fine. x is 5 mph faster than y and y is 5 mph slower than x mean the same thing. Hope that helps!

[mozart611]

I did mine similar to the alternate method but with a slight twist. Since Liam would have arrived on time if he went at the hypothetical rate, i made the hypothetical time t and the actual time t -1/15 since he arrived 4 mins before he was to start

_______Rate___X___Time___ =___Distance
Actual___r__________30/r_________ 30
Hyp____r - 5 ______30/(r-5)________30

equation set-up, 30/r - 1/15 = 30/ (r - 5)

I don't understand how my interpretation of the times is incorrect, can you please explain it to me?

Thanks

[thatsku]

I did mine similar to the alternate method but with a slight twist. Since Liam would have arrived on time if he went at the hypothetical rate, i made the hypothetical time t and the actual time t -1/15 since he arrived 4 mins before he was to start

_______Rate___X___Time___ =___Distance
Actual___r__________30/r_________ 30
Hyp____r - 5 ______30/(r-5)________30

equation set-up, 30/r - 1/15 = 30/ (r - 5)

I don't understand how my interpretation of the times is incorrect, can you please explain it to me?

Thanks

Mozart611,

You have to know that your equation is equivalent to 30/r - 30/(r-5) = 1/15

however, 30/(r-5) is actually the larger value, so 30/r - 30/(r-5) is actually a negative value...

Hope that helps...

[thatsku]

_______Rate___X___Time___ =___Distance
Actual___r__________30/r_________ 30
Hyp____r - 5 ______30/(r-5)________30

equation set-up, 30/r = 30/ (r - 5) - 1/15

That's actually how I've set up my equation but keep getting r^2 - 5r - 2250 = 0 versus the r^2 + 5r - 2250 = 0 that's in the book.

Can someone please help?

Thanks!

[thatsku]

Nevermind... got it...

[Ben Ku]

Okay ... if you have further questions, please post!