Math Help - interesting puzzle

1. interesting puzzle

A and B run in opposite directions from a pt. P on a circle with different but constant speeds. A runs in clockwise direction. They meet for the first time at a distance of 900 m in clockwise direction from P and for the second time at a distance of 800 m in anticlockwise direction from P. If B is yet to complete one round, the circumference of the circle is
a) 1700m b) 1250m c) 1300m d) 1200m

2. Originally Posted by bharathlece
A and B run in opposite directions from a pt. P on a circle with different but constant speeds. A runs in clockwise direction. They meet for the first time at a distance of 900 m in clockwise direction from P and for the second time at a distance of 800 m in anticlockwise direction from P. If B is yet to complete one round, the circumference of the circle is
a) 1700m b) 1250m c) 1300m d) 1200m
If I have done this right 1300m.

Now if you tell us what you have done on this and where you are having
difficulties you might get some help in how to solve this sort of problem.

RonL

3. I Have Approached In Follwing Way

A and B run in opposite directions from a pt. P on a circle with different but constant speeds. A runs in clockwise direction. They meet for the first time at a distance of 900 m in clockwise direction from P and for the second time at a distance of 800 m in anticlockwise direction from P. If B is yet to complete one round, the circumference of the circle is

I TOUGHT TOTAL CIRCUMFERENCE OF CIRCLE IS X

1 ST A -> 900

B -> X-900

2ND A-> X-800

B-> 800

THEN WHAT TO DO HEAR IS MY DOUBT

PLZ SAY ANS IN BRIEF

4. Originally Posted by bharathlece
A and B run in opposite directions from a pt. P on a circle with different but constant speeds. A runs in clockwise direction. They meet for the first time at a distance of 900 m in clockwise direction from P and for the second time at a distance of 800 m in anticlockwise direction from P. If B is yet to complete one round, the circumference of the circle is
a) 1700m b) 1250m c) 1300m d) 1200m
Let the circumference be {math]C[/tex], and the two speeds be
$v_A$ and $v_B$, then when they meet for the
first time:

$
(v_A+v_B)t_1=C
$
,

but we also know that:

$v_At_1=900$,
and:
$v_Bt_1=C-900$.

These three equations may be used to generate two equations which
do not contain $t_1$:

$
\frac{C}{v_A+v_B}=\frac{900}{v_A},\ \frac{C-900}{v_B}=\frac{C}{v_A+v_B}
$
$....(Eqs\ 1)$.

Also when they meet for a second time:

$
(v_A+v_B)t_2=2C
$
,

but we also know that:

$v_At_2=2C-800$,
and:
$v_Bt_2=800$.

These three equations may be used to generate two equations which
do not contain $t_2$:

$
\frac{2C-800}{v_A}=\frac{2C}{v_A+v_B},\ \frac{800}{v_B}=\frac{2C}{v_A+v_B}
$
$....(Eqs\ 2)$.

The value of $C$ can be easily found for these two sets of equations.

RonL

5. thank u sir

thank u sir , for ur replay.