Nanyang Girls’ High School

    Secondary 1 Mathematics

    Enrichment 2003

    Algebra: Challenging problems

    The following questions are taken from an article written by Tom M. Giambrone, from Indiana University Pennsylvania.

    1. Omar the Rope Maker decided to make a rope long enough to stretch around the Earth (the

    circumference of which is 40000 kilometers). Having completed the task, he discovered that he

    had actually made the rope 12 metres too long. Now wanting to cut the rope (it was somewhat of a

    record length), he decided to put the ends of the rope together and have all his relatives help him

    hold the rope and equal distance off the ground all the way around the earth. Which of these

    animals could pass under the rope: (a) ant, (b) snake, (c) Omar, (d) adult elephant, (e) blue whale?

    2. A contractor constructed a brick wall. He employed one bricklayer who could build the wall in ten

    hours and another bricklayer who could build the wall in 9 hours. Working together, the

    bricklayers laid 10 fewer bricks an hour than is they had worked independently. It took them

    exactly 5 hours to build the wall. How many bricks are in the wall?

    3. 2 ferryboats started at the same instant from opposite sides of a river, traveling across the water at

    right angles to the shore. They first met 720 yards from the nearest shore and, on reaching the

    opposite side, spent 10 minutes in the slip before starting back. They met again 400 yards from the

    nearest shore. What is the width of the river?

    4. A little boy liked to play on the ‘up’ escalator of a department store. When he walked up the

    escalator, he counted 10 steps and the trip took 20 seconds. When he ran down, he counted 50

    steps and the trip took 30 seconds. How many steps of the escalator were visible at one time?

    5. Consider this fortunate incident. A girl was crossing a railroad bridge when, halfway across, she

    saw a train 50 metres away moving toward her. She immediately turned and ran so that the train

    missed her by the narrowest of margins. If she had tried to cross the bridge, the train would have

    struck her one metre before she could have reached the end. How long is the bridge?

NYGH/THK/Enrichment/Algebra/2003