Phoenix9 wrote:
Hi All,
I have a question regarding a problem from Manhattan Strategy Guide: Word Translations (3).
Chapter 2. Rates. Page 37.
Problem:
Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 30 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
Solution:
Of the many ways to solve this problem, two are as follows:
(Method 1)
Assume the actual speed of Liam to be r. Distance travelled is 30 miles. So, time taken is 30/r. In the hypothetical case, speed of Liam is (r-5). Distance remains the same. So, time taken is (30/r)+(1/15) because 4 minutes is 1/15th hour. So, translating these values into equations, the hypothetical scenario becomes:
distance = speed * time
30 = [(30/r)+(1/15)]*[r-5] => 30 = [(450+r)/15r]*[r-5] => 450r = [450+r][r-5] => r^2 -5r-2250 = 0 => (r-50)(r+45) = 0 => r = 50.
(Method 2)
This is the method used in the Manhattan guide. Speed in the actual case is considered to be (r+5). Time taken is therefore 30/(r+5). Speed in the hypothetical case is considered to be r. Time taken is 30/r. Because we know time taken in the hypothetical scenario is 4 minutes more, 30/r = [(30/(r+5))+(1/15)] => 30/r = [((450+r+5)/(15r+75)] => 30(15r+75) = r(455+r) => r^2 +5r-2250 = 0 => (r+50)(r-45) = 0 => r=45.
Can anyone please explain to me why both these methods DON'T yield the same answer? Isn't the first method more appropriate because the hypothetical scenario is the one in which we should assume the speed to be 5mph less than the actual and time taken is 4 minutes more than the actual?
Thanks.
Hi all,
I'm reviewing rates & work and even though I feel I pretty much got it figured out, questions like this one let me doubt myself.
My question for this one is: Phoenix9 introduced 2 approaches to solve the question that use the information given differently, in approach 1 the fact that Liam should go 5mph slower is marked as (r-5) in the hypothetical case. In approach 2 it's (r+5) in the actual case. No questions until here.
I, however, tried like this:
Real case: R: r+5 ; T: (30/r - 1/15); Hypothetical case: R: R ; t: (30/r)
The equation than comes to two negative values for r, which is unsolvable.
My question is: what's the mistake in my approach?
Thanks
Christian