Question

Jane and Jillian are hiking around a hill and one complete circle is 8 miles long. They start together but hike in opposite directions. Both start to hike at 8:00 AM. Jane's hiking speed is 3 mph and Jillian's hiking speed is 5 mph. How long will it take before they meet? At what time will they meet? In how many hours? What time will they meet at?

Answer 1

It will tale 1 hour before they meet and they will meet agin at 9 :00 AM.

Explanation:

Speed of Jane,
`v_1=3` mph

and the speed of Jillian,
`v_2= 5` mph.

Length of one complete circle = 8 miles.

Both are moving in the opposite direction, let the starting point is at O, and met at the point P after time, t, as shown in the figure.

Let the length covered by Jane via path OAP= x miles.

`\Rightarrow x= 3t` [as distance= speed x time]

`\Rightarrow t=x/3 \cdots(i)`

The length covered by Jillian via path OBP
`= 8-x` miles

`\Rightarrow 8-x= 5t` [as distance = speed x time]

`\Rightarrow t=(8-x)/5 \cdots(i)`

Now from equation (i) and (ii),

`(x)/(3) = (8-x)/(3)`

`\Rightarrow 5x=3(8-x)`

`\Rightarrow 5x+3x=24`

`\Rightarrow x=3`

So, the distanc covered by Jane = 3 miles and

the distanc covered by Jillian = 8-3=5 miles

From equation (i), time taken, t = 3/3= 1 hour.

So, it will tale 1 hour before they meet.

As the startion time was 8:00 AM, so the will agin meet at 9 :00 AM.