SOLUTION: Nora leaves Town A and walks towards Town B at a speed of 100m/min. At the same time , Kate and Lixin walk from Town B towards Town A at a speed of 80mm/min and 75m/min respectivel

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Question 1061532: Nora leaves Town A and walks towards Town B at a speed of 100m/min. At the same time , Kate and Lixin walk from Town B towards Town A at a speed of 80mm/min and 75m/min respectively. If Nora meets Lixin 6 minutes after passing Kate, find the distance between Town A and Town B.
Please help me this one!! I need it now!! Thank you.
Found 4 solutions by ikleyn, Sam91, MathTherapy, greenestamps:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website!
.
Nora leaves Town A and walks towards Town B at a speed of 100 m/min. At the same time , Kate and Lixin walk from Town B towards
Town A at a speed of 80 m/min and 75 m/min respectively. If Nora meets Lixin 6 minutes after passing Kate,
find the distance between Town A and Town B.
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Let L be the distance between the cities and let "t" be the time (in minutes) from the start to the moment Nora meets Kate. The first equation is 100*t + 80*t = L (1) (Nora's walked distance + Kate's distance = L at the moment they meet each other) Also, the time from the start to the moment Nora meets Lixin is (t+6) minutes. And the second equation is similar to the first one: 100*(t+6) + 75*(t+6) = L. (2) (Nora's walking distance + Lixin's distance = L at the moment they meet each other) Equations (1) and (2) have equal right sides. Hence, their left sides are equal, too: 100*t + 80*t = 100*(t+6) + 75*(t+6). It is a single equation for one unknown "t". Simplify and solve for "t": 180*t = 175t + 600 + 450, 180t - 175t = 1050, 5t = 1050, t = = 210. Thus we found the time "t" till the first meeting. It is 210 minutes. Then the distance between the cities, according to the equation (1), is 100*210 + 80*210 = 37800 meters = 37.8 kilometers. Answer. The distance between the cities is 37800 meters, or 37.8 kilometers.

Answer by Sam91(1)   (Show Source):
You can put this solution on YOUR website!
Let d be the distance (in meters) between cities A and B.
Time in minutes and speed in meters per minute (m/ min)
Using formula, distance = speed * time
d= v * t
let @ time t minutes Nora meets Kate.
d= 100*t + 80*t
d= 180* t (1)
('d' is point @ kate and nora meet each other= Distance covered by Nora + distance covered Kate)
Similarly, @ time (t+6) minues Nora meets Lixin
d= 100*(t+6) + 75*(t+6) ( here (t+6) is common)
d= 175*(t+6)
d= 175*t + 1050 (2)
Equating (1) and (2)
d = d
180 t = 175 t+ 1050
On simplifying,
180t - 175t = 1050
5t = 1050
t=210 minutes
@ time = 210 minutes Nora met Kate
Also,@ time (210+6=) 216 minutes Nora met Lixin
Using, the value to t and substituting in equation (1)
d= 180* 210 m (here minutes will be cancelled by minutes)
d= 18*21*100 m = 37800 metrea
The distance between the cities A and B is 37800 meters.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Nora leaves Town A and walks towards Town B at a speed of 100m/min. At the same time , Kate and Lixin walk from Town B towards Town A at a speed of 80mm/min and 75m/min respectively. If Nora meets Lixin 6 minutes after passing Kate, find the distance between Town A and Town B. Please help me this one!! I need it now!! Thank you. ********************************************************************************** ----- what is written at this line and below it, is written/added by me, tutor @ikleyn ----- **********************************************************************************
I added it here, because the solution by tutor @MathTherapy is incorrect. So, I simply copied-pasted the solution by @MathTherapy and pointed/commented that place, which is incorrect. <<<---=== this equation is INCORRECT (mine, @ikleyn's comment) It is written (it is valid) under the assumption that only Nora is moving, while Kate stands unmoved; but it is not so. Therefore, everything that follows in the @MathTherapy post, is invalid. ********************************************************************************** I know the tutor @MathTherapy as very accurate tutor at this forum. Dear @Math Therapy, if you decide to take off your post, may be, it will be the best decision - I will not have any objections against it. Because my greatest goal is to keep this forum as clean as possible (as I can). By the way, my original (very old, ~ 10 years ago) solution to this problem is the post number 1 in this bunch of posts. So, had I place these my notes under my old solution, the chance would be great that nobody sees it. It is why I placed my notes here . . . You're right, @IKLEYN. I did the problem as though it had stated, "If Nora takes 6 mins to GET to the POINT where Lixin was when Nora and Kate MET," instead of, "If Nora meets Lixin 6 minutes after passing Kate........" I EDITED the post, and REPOSTED the CORRECT solution! Let time taken for Kate to meet Nora, and vice versa, be T Since Nora left Town A and Kate and Lixin left Town B at the same time, distance Nora covered, when she met Kate = 100T Also, distance Kate covered, when she met Nora, coming from Town B = 80T When Nora and Kate met, both had covered the entire distance between Towns A & B Therefore, distance between Towns A & B = 100T + 80T = 180T At the same time that Nora and Kate met, Lixim, coming from Town B, had covered a distance of 75T When Nora met Kate, Nora had traveled a distance of 100T. After meeting Kate, Nora then traveled an additional 6(100), or 600 m for a total of 100T + 600 m, when she and Lixin met Likewise, when Nora met Kate, Lixin had traveled a distance of 75T. 6 minutes thereafter, Lixin traveled an additional 6(75), or 450 m for a total of 75T + 450 m, when she and Nora met Therefore, when Nora met Lixin, both had traveled a combined 100T + 600 + 75T + 450, the distance between the 2 towns And, since the distance between the 2 towns is 180T, we get: 100T + 600 + 75T + 450 = 180T 175T + 1,050 = 180T 1,050 = 180T - 175T 1,050 = 5T Time taken for Nora and Kate to meet/Lixim to cover 75T, or mins Thus, distance between Towns A & B = 180T, or 180(210) = 37,800 m

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

I will assume that Kate's rate is in fact 80 m/min and not 80 mm/min....!

Nora and Kate together, walking at rates of 100 m/min and 80 m/min, cover the whole distance in a certain amount of time.

Let t be the number of minutes it takes Nora and Kate to meet. Then the distance between the two towns is 180t.

In the time it takes Nora and Kate to meet, Nora and Lixin together, traveling at rates of 100 m/min and 75 m/min, cover a distance of 175t.

The fraction of the total distance between the two towns that Nora and Lixin together cover in t minutes is 175t/180t = 35/36. So the fraction of the total distance remaining to be covered for Nora and Lixin to meet is 1/36.

The additional time required for Nora to meet Lixin is 6 minutes, so the time needed for Nora and Lixin to meet is 36*6 = 216 minutes.

The combined speed of Nora and Lixin is 175 m/min, so the distance between the two towns is 216*175 = 37800 m.

ANSWER: 37800 m

As a check, note that the distance between the two towns can also be calculated as the amount of time Nora and Kate travel before meeting times their combined rate. The two of them met after 216-6 = 210 minutes, so....

210*180 = 37800