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.