Question

A man set out at noon to walk from a to b and a friend of his started at 2pm on the same day to walk from b to a. They met on the road at 4:05pm, and each man reached his destination at exactly the same time. Can you say at what time they both arrived?

Answer 1

Answer:

I think the answer is 8:10 pm.

Not sure.

Answer 2

Conclusion

Time Average

The values in a sample are averaged over time by the Time Average algorithm. The Time Average algorithm considers the interval of time between value changes as opposed to the Average algorithm, which divides the total of the sample's values by the total number of values.

Main solution

It took person 1  4hrs min. to reach C

(C is the place where they meet)

Assume A to B is 1km

A to C = x

C to B = 1-x km.

at 2 pm, Person 1 covered

Speed for $1 = \frac{x}{4hrs. 5min.} = \frac{x}{4\frac{1}{12} } km/h$

at 2 p.m 1 covered $\frac{x}{4\frac{1}{12} } \times 2 = \frac{2x}{4\frac{1}{12}}km$

Person 2 = $\frac{1-x}{2\frac{1}{12}} km/h$

They take exact time to reach destination.

$\therefore$ Speed $= \frac{D}{T}$ and $T = \frac{Distance}{Speed}$.

Person 2 : Distance = x.  speed = $\frac{1-a}{2\frac{1}{12}}$

T = x $\times \frac{2\frac{x\1}{12} }{1-x}= \frac{2\frac{1}{12}x }{1-x}$

Person 1 = Distance = 1 - x  speed = $\frac{x}{4\frac{1}{12} }$

T = 1 -x $\times \frac{4 \frac{1}{12} }{x} = \frac{4\frac{1}{12} - 4\frac{1}{12}x }{x }$

$\frac{2\frac{1}{12} x}{1-8} = \frac{4 \frac{1}{12}- 4\frac{1}{12}x }{x}\\2\frac{1}{12} x^2 = 4\frac{1}{12} x - 4\frac{1}{12}x+4\frac{1}{12}x^2.\\\\= 2x^2 = 4\frac{1}{12} - 8\frac{1}{6} \\-\frac{2}{-2} x^2 - \frac{4\frac{1}{12} }{-2} + \frac{8\frac{1}{6} }{-2} x=0\\\\x = \frac{-(-4\frac{1}{12} )\pm\sqrt{(4\frac{1}{12} )^2 - 4 \times 2\frac{1}{24} } }{2}\\x = \frac{+(4.0833)\pm \sqrt{4.0833^2 - (4\times2.0417)} }{2} \\x = \frac{4.0833 \pm \sqrt{8.565} }{2} = \frac{4.0833 \pm 2.917}{2}$

x = 0.58315 hrs km or 7.0003 hr km

Since it was assumed that the entire journey is 1 km, then 0.58315 holds as the valve of  x since it is below 1km.

Thus, $T = \frac{2 \frac{1}{12} \times 0.58315 }{1 - 0.58315} = \frac{2.08333\times0.583}{1-0.5815} \\= \frac{1.2149}{0.1685} = 2.91 hrs = 2 hrs. 55 min.$

Thus the arrival time is :

 4 : 05

+2: 55

= 7:00 p.m

So, the arrival time is 7:00pm

To learn more about Time Average

https://brainly.in/question/17786891

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