Saturday, July 11, 2009

Math problems of the week: 1930's Algebra vs. Interactive Math Project

1. The last three word problems (of 10 in all) from Chapter 2 of A Second Course in Algebra, (originally published in 1937), p. 84-5

Two boys took a trip into the country on a bus which average 18 miles per hour. They walked home over the same route at the rate of 4 miles per hour. The entire trip took 3 hours and 40 minutes. How far did they go?

A boy can row 15 miles upstream and back in 8 hours. His rate upstream is 3/5 of his rate downstream. Find his rate downstream.

A train traveled 180 miles from P to Q. Forty-five miles from Q it met with an accident which delayed it 30 minutes. It then continued at half its usual speed and arrived at Q two hours late. What is its usual speed?

2. The only three word problems in the most closely matching problem set in Interactive Mathematics Program, Year 4 (Chapter 4 ), p. 287

An Average Drive

Amparo took a trip on a warm, sunny day to her favorite spot overlooking the ocean. That spot was 100 miles from home. Amparo knew that in order to be home on time, she needed to average 50 miles per hours for her overall trip.

1. As Amparo reached her destination, she realized that she had made good time while still staying within the legal speed limit. She figured out that she had averaged 60 miles per hour on her trip there. What should Amparo's average speed be on the return trip so that her average speed for the round trip will be 50 miles per hour.
(Warning: The answer is not 40 miles per hour!)

2. On another trip to the same spot, Amparo took a more leisurely pace. When she reached her destination, she realized she was late! She had averaged only 25 miles per hour getting there. What should Amparo's average speed be on the return trip so that her average speed for the round trip will be 50 miles per hour?
(Warning: The answer is not 75 miles per hour!)

3. Amparo makes this round trip frequently, and her goal is to average 50 miles per hour for the round trip. However, her average speed for the trip to the ocean varies.

Let x be her average speed (in miles per hour) on the way to the ocean. Find an expression in terms of x that tells Amparo what her average speed should be on the return trip for her average speed for the whole trip to be 50 miles per hour.

3. Extra Credit
After they successfully complete the second problem set, how likely do you think it is that Interactive Math Program students will be able to do the first problem set without hints?

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