01 Sep '18 05:03>
Hint:
total distance = average_speed * total_time
total distance = average_speed * total_time
Originally posted by @iamatigerInteresting stuff.The Algebra is a bit too complicated for me but I can just about see how it works.
The answer
Sorry, there is no easy way of hiding a multiple line post.
The first journey takes 1 hour and is driven at two speeds s1 and s2
We are given an equation for the average speed of this journey
A =(s1+ s2)/2
Since the time is 1 hour, if our speeds are in mph then
Distance in miles = D = (s1 + s2)/2
(We can also work out that the times ...[text shortened]... wife’s second journey must have taken longer than 1 hour, but less than 1 hour and 30 minutes.
Originally posted by @iamatigerRight then.I remember spending hours on this one , but never worked out how to do it.Here goes:-
Sounds challenging!
Originally posted by @iamatigerThe answer in the book isn't that far but as I said, the question is a bit vague and the book doesn't give any working out.I'll let you think about it and maybe make other assumptions and then give the quoted answer when you(or someone else) has had another go.
Looks like the back of the army has to travel 75 miles
Assume the army travels at speed a, and the messenger travels at ka
Army total time = 75/a
Messenger time to front = 25/(ka-a)
Messanger time to back = 25/(ka+a)
Messenger total time = (25/a)(1/(k-1)+1/(k+1))
Messenger time = army time so
75/a = (25/a)(1/(k-1)+1/(k+1))
Divide by 25/a
3 = 1/( ...[text shortened]... distance = orderly speed x time = ka*75/a=75a
Orderly distance = 25*(1+sqrt(10))=104.0569 miles
Originally posted by @iamatigerIt is!!.
Ok, let's assume that the army stops when the general has gone 50 miles.
This changes the calcs as follows:
Assume the army travels at speed a, and the messenger travels at ka
Army total time = 50/a
Messenger time to front = 25/(ka-a)
Messanger time to back = 25/(ka+a)
Messenger total time = (25/a)(1/(k-1)+1/(k+1))
Messenger time = army time ...[text shortened]... ly speed x time = ka*50/a=50k
Orderly distance = 25*(1+sqrt(5))= 80.9017 miles
is that right?
Originally posted by @vendaThanks 😀
It is!!.
Well done!!
Your Algebraic talents are impressive.
I'll study your solution in detail when I have a bit of time and see what I can learn.
Perhaps when I'm trying to fill a bath with the plug out!!