A 30-meter by 70-meter rectangular garden is surrounded by a walkway with a width of 5 meters. Karen is running one lap around the outer edge of the walkway at a rate of 4 km per hour, while her brother is running 2 laps around the inner edge of the walkway twice faster. If they start running at the same time, how many minutes earlier will Karen's brother finish his run?

Step-by-step explanation:

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The garden measures 30m × 70m. The perimeter would be

Perimeter = 2(30 + 70) = 200m

If Karen's brother is running 2 laps around the inner edge of the walkway, then the total distance covered is 200 × 2 = 400m

Converting to km, it becomes

400/1000 = 0.4km

If he runs 2 times faster than Karen, then his speed is 2 × 4 = 8km/h

Time = distance/speed

Time spent in running the 2 laps is

0.4/8 = 0.05 hours

Converting to minutes, it becomes

0.05 × 60 = 3 minutes

Since the walkway is 5m, if Karen is running one lap around the outer edge of the walkway, the total length would be (70 + 5 + 5) = 80m

The width would be (30 + 5 + 5) = 40m. The perimeter is

2(80 + 40) = 240 m

Converting to kilometers, it becomes

240/100 = 0.24 km

Time taken by Karen to run 0.24km is

0.24/4 = 0.06 hours

Converting to minutes, it becomes

0.06 × 60 = 3.6 minutes

The difference in time is

3.6 - 3 = 0.6 minutes

Karen's brother finish his run in

0.6 minutes earlier than Karen.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

true

step-by-step explanation:

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