The total length of a wall along the front and one side of a rectangular parking

Question

The total length of a wall along the front and one side of a rectangular parking lot is 240 feet. If the front wall is twice as long as the side wall, how many feet long is the side wall? A. 240 B. 160 C. 120 D. 80 E. Not Given A carpenter has a piece of lumber measuring 6 feet 5^3/4 inches long. How much must the carpenter saw off to be left with a piece 4 feet 10^5/16 inches long? A. 1 foot 7^7/16 inches B. 1 foot 6^7/16 inches C. 1 foot 2^1/8 inches D. 2 feet 7^7/16 inches A racetrack measures 10 miles long. If an automobile completes the course once in exactly 4 minutes, what is the average rate of speed in miles per hour? A. 50 B. 100 C. 150 D. 200 E. 250 What is the prime factorization of 60? A. (1) (60) B (2) (30) C. (2) (5) (6) D. (2) (2) (3) (5) E. Not Given If the 3-digit number 27d, in which d is the one's digit, is evenly divisible by both 3 and 4, what is the value of d?

Explanation / Answer

A. Let the length of side wall be x.

Then the length of the side wall = 2x.

x + 2x = 240

=> 3x = 240

=> x = 240/3

=> x = 80ft.

B. Total length of lumber = 6 ft 5 3/4 inches

= 6 * 12 + 5 3/4 inches

= 77 3/4 inches

Length remaining = 4 ft 10 5/16 inches

= 4 * 12 + 10 5/16 inches

= 58 5/16 inches

=> Length to be chopped

= 77 3/4 - 58 5/16

= (77*4+3)/4 - (58*16+5)/16

= 311/4 - 933/16

= 1244/16 - 933/16

= 311/16

= 19 7/16 inches

= 1 ft 7 7/16 inches

C. Total distance = 10 miles

Time taken = 4 mins = 4/60 = 1/15 hours

=> Average speed

= 10 / 1/5

= 50 miles/hr

D. 60 = 4 * 15

= 2 * 2 * 3 * 5

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