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4 years ago

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Jane and Jillian are hiking around a hill and one complete circle is 8 miles long. They start together but hike in opposite dire

ctions. 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?

1 answer:

Jlenok [28]4 years ago

3 0

Answer:

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

Step-by-step 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),

$\frac{x}{3} = \frac{8-x}{3}$

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

$\Rightarrow 5x+3x=24$

$\Rightarrow x=3$

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.

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