Jim Gould

Hi Jim, and welcome to WardsWiki. Just a quick question - are you sure that this material is appropriate here? To judge, could you have a quick look at the pages listed on NewUserPages and WelcomeVisitors. That'll give you a good feel for the sorts of things that happen here. Thanks.

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Grade Seven
 Patterns, Functions and Algebra Standard
     Use of Algebraic Representations
       Indicator Number 8: Use formulas in problem-solving situations

Learning Objective for Lesson: Students will learn to solve rate-time-distance word problems when the motion (rate or speed) remains the same.

Rate x Time = Distance

Suppose you and a friend live three miles apart. While talking on the phone, you decide to start walking toward one another at the same time. Let’s say noon. You walk at the rate of two miles per hour, and your friend walks at four miles per hour. When will you meet?

Your distance plus your friend’s distance = three miles

Your Rate x Time plus your friend’s Rate x Time = three miles

2mph x T + 4mph x T = 3m

(where “mph” means “miles per hour” and “m” means “miles”; these are standard units)

6mph x T = 3m

(6mph x T) / (6mph) = 3m / (6mph)

T = 3/6 hours = ½ hour

Note how dividing the units worked: miles / (miles per hour) = hours.

Therefore, you meet your friend half an hour after noon, i.e., at 12:30 p.m. (I hope this is correct; it’s been a while!)

Now it’s Your turn!

Make up your own R x T = D problem and post it on this wiki. It can be trains, planes, automobiles, riding lawnmowers, bicycles, inline skaters, etc. But, for now, make the starting time the same.

 Enter Your Problem Here, please.

Next time, we’ll see what happens when the starting times are different. Here’s a hint: if Person A leaves at noon and Person B leaves at 12:15, Person A’s time is T + ¼ hours and Person B’s time is T.

[Note for Jim: I have fixed certain faults in the above for you, but I feel the example is unbalanced. You should explain the How and Why aspects of tackling such problems, and point out where errors might have occurred. Please avoid insulting their intelligence by implying that something useful will be learnt by replacing “walking” with flying, driving, cycling, etc. Instead, just explain why the mode of travel doesn’t matter. I feel that a more subtle problem could have been solved, so that one sees that the algebra is really valuable. In the above example, some will find the algebra boring, since they can just “see” the answer anyway! Also, it’s far too early to start inventing further examples. Even if they can produce trivial variations of the problem, that’s not a good way to proceed.]