There is a point P somewhere b/w points A and B. 2 persons start from P in opposite direction, reach endpoints

Question

A, B respectively and move back and meet again at P. Then, is it always true that they have traveled for same time, given that their speeds are different?

1)They travel with diff. but constant speeds.

2)They donot stop in between

3)ironduke, its given that they meet again at same point P, not given that they meet after same time.

Answer 1

For their travel time to be the same, it would depend on the distance from point P to A and point P to B plus the corresponding travelling speed of the two person.

let's say person X travels from P to A and back to P,
meanwhile person Y travels from P to B then back to P.

example 1

should point P be in the middle of endpoints A and B, person X and Y cannot have the same travelling time should they have different speeds.
let's say the distance is 30km ( P is the midpoint of A and B), X travels at 20km/h while Y travels 30km/h. it's obvious Y will have a shorter travelling time.


example 2

distance of P to A = 10km
distance of P to B = 20km
X travels at 10km/h while Y travels at 20km/h.
thus both X and Y will have the same travelling time of 2 hours.

therefore you can conclude that TRAVELLING TIME IS NOT ALWAYS THE SAME.

Answer 2

Let a = speed of A, b = speed of B, t = time traveled, d = the same distances traveled by A and B to endpoints.

The formula to compute the same travel time they meet at point P.
at = bt
t = a(1/bt)
t = a/bt
t^2 = a/b
t = √a/b

It is always true that they reach P with the same travel time although their speeds are different.

Moving back point P will not be same as the point P during the 1st meeting. Their travel time however would be the same even if they traveled with different speeds.

Answer 3

Remember that D = V*t.

If P is located in the exact center, the two persons need to have the same velocity. But this is a restriction.

Yet if P is on 1/3 of the distance from A to B, for example, then it is true that:

AP = 1/3 AB, and

PB = 2/3 AB

So, for Person traveling from P to B and back needs to be traveling twice as fast as the other to make it back at the same time.

For the same time traveled, d=vt, you need to increase one variable coefficient and decrease the other variable coefficient by the same constant.

Person 1: d = v * t

Person 2: any combination of D = V * t

D / n = n * V * t, where n is any positive number, not zero

and d + D/n = distance from A to B.

Assign numbers to variables.

A ---------- P -------------------- B
|........20....|.............. 40...........|

For a given time t = 10 sec, for example, then velocity of Person AP would be 2 units per sec ( 20 / 10 sec ).

And Velocity of person BP would be 4 units per sec ( 40 / 10 sec), twice as fast as AP, traveling twice the distance. IN THE SAME TIME

Answer 4

Let's take a case. Let's say P is 5 miles from A and 10 miles from B. Let's say person X goes at 50 mph to A and back...and person Y goes at 60mph to B and back.

Person X will travel 10 miles at 50mph, so 1/5 of an hour total travel time will elapse.

Person Y will travel 20 miles at 60mph, to 1/3 of an hour total travel time.

Gee, guess not.

Answer 5

no, that's not true that they traveled for the same amount of time. P could have been one mile away from A and 5 miles away from B, so if B was hauling some serious *** and A was just poking along, it's possible that although B is much further from P than A, B could beat A there and back. (Am I right?)

Answer 6

If A and B meet at exactly the same time, then of course they will have both traveled the same amount of time.

If they both start at noon and then meet precisely at 1:00PM, then they both have traveled for 1 hour.

Answer 7

In reality the possible answer for this question is 'May be'.