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    1. if j, k, and t represent whole numbers, and n = 5j^2=3k^3=2t. What is the smallest possible value of n when n > 0?

    2. Tex and Roy are going from Deadwood to Dodge City, but they have only one horse. They know that there are some equally spaced water holes between the towns, so they agree on this scheme:
    They will start out together, with Tex riding and Roy walking. When Tex gets to a water hole, he ties up the horse for Roy, and he continues forward on foot. They follow this scheme, alternating walking and riding, until they finally reach Dodge City at the same time.
    The two of them ride at the same rate, and walk at the same rate.
    If they ride 3 times as fast as they walk, for what fraction of the time for the whole trip was the horse resting at water holes? ("Algebra" is not needed)

    3. A contractor knows that one of his bricklayers would take 9 hours to build a chimeny, and his other bricklayer would take 10 hours to do the job. He also knows that when they work together they talk a lot, and their combined output is decreased by 10 brickes per hour. But since he is in a hurry to have the chimeny built, he assigns both men to the job. They complete the job in 5 hours. How many bricks are in the chimney? (("Algebra" is not needed)

    © BrainMass Inc. brainmass.com December 24, 2021, 8:37 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/smallest-possible-value-295128

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    1. if j, k, and t represent whole numbers, and . What is the smallest possible value of n when n > 0?
    2. Tex and Roy are going from Deadwood to Dodge City, but they have only one horse. They know that there are some equally spaced water holes between the towns, so they agree on this scheme:
    • They will start out together, with Tex riding and Roy walking. When Tex gets to a water hole, he ties up the horse for Roy, and he continues forward on foot. They follow this scheme, alternating walking and riding, until they finally reach Dodge City at the same time.
    • The two of them ride at the same rate, and walk at the same rate.
    • If they ride 3 times as fast as they walk, for what fraction of the time for the whole trip was the horse resting at water holes? ("Algebra" is not needed)
    3. A contractor knows that one of his bricklayers would take 9 hours to build a chimney, and his other bricklayer would take 10 hours to do the job. He also knows that when they work together they talk a lot, and their combined output is decreased by 10 bricks per hour. But since he is in a hurry to have the chimney built, he assigns both men to the job. They complete the job in 5 hours. How many bricks are in the chimney? (("Algebra" is not needed)

    1

    The way to answer this is to start with the highest power. All cubed numbers will have prime factors in triplicate. My first guess was n=3(53x33x23), which means k=30. But we also have to look at what j could be. Numbers that are squares will have their prime factors in pairs. n=5(52x34x23) but since there's an odd number of 2's, the number in brackets is not square. But, if we multiply this guess by 8 (=23), then n/3 is a cube and n/5 is a square.

    2 Let us suppose that it takes x minutes to ride to a watering hole. Therefore, it takes 3x minutes to walk. At t=0 minutes, both Tex and Roy are at Deadwood. At t=x minutes, Tex arrives at the first watering hole, hitches the horse and begins to walk, while Roy is 1/3 of the way there. At t=2x minutes, Tex is 1/3 the distance between watering holes, and Roy is 2/3 the distance between Deadwood. At t=3x minutes, Roy arrives at the first watering hole and gets the horse. Tex is 2/3 the distance between the watering holes. At t=4x, both Tex and Roy arrive at the second watering hole. Since they are both at the same point, the pattern can repeat. Since it took 4x minutes for both to reach this point and the horse was waiting at the first watering hole for 2x minutes, the horse was waiting half the time. The pattern repeats until they reach Dodge City. If there were an even number of watering holes, then Roy and Tex would not arrive at the same time, which doesn't happen. (Tex and Roy would meet at the last watering hole and Tex, with the horse, would arrive sooner than Roy). So, there are an odd number of watering holes, and the pattern continues to Dodge City. The horse waits half the time during the journey.

    3 Let x be the number of bricks in a chimney. Bricklayer 1 (B1) works at a rate of x/10 per hour and B2 works at a rate of x/9 per hour. The bricklayers working together takes 5 hours to finish the chimney but their work rate decreases by 10 bricks. Thus, we have this equation:

    Therefore, the chimney has 900 bricks.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:37 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/smallest-possible-value-295128

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