Aden and John started jogging along a circular track. Aden started at Point X while John started at Point Y where the line XY formed the diameter of the circle. Aden and John jogged towards each other along the circular track from their respective starting point and first met at Point W which was 80 m from Point X. After they met for the first time, they continued jogging along the track and finally met again for the second time at Point Z which was 60 m from Point Y. Find the distance of the circular track.

X
A1 [ 80 ] **Half a circle to meet the first time**
[ ] J1
Y
A2 [ ]
[ 60 ]
[ ] Z **A circle to meet the second time**
[ ] J2
DA1 --> 80 m
DA2 --> 2 x 80 m = 160 m
160 - 60 = 100 m **W to Y**
100 + 80 = 180 m **XY (1/2 circular track)**
180 x 2 = 360 m
The distance of the circular track was 360 m.
I have an alternative method...hope that mine is correct...

ReplyDeleteDistance travelled by Aden when met for 2nd time = 2 x 80 = 160

Distance travelled by John when met for 2nd time = 2 x 60 = 120

Difference in the distance = the distance of W and Y = 160 - 120 = 40

distance of semicircle = 80 + 40 + 60

= 180

Distance of circle = 180 x 2 = 360 m

Although answer is correct, but the workings are not correct.

ReplyDelete"Distance travelled by John when met for 2nd time = 2 x 60 = 120"

John actually jogged faster. He jogged 300 m (= 360 - 60)while Eden only jogged 240 m (= 180 + 60)when they met the second time.

I don't understand without the aid of a diagram...

ReplyDelete