Solving a Typical Rate-Time-Distance Problem
Date: 09/02/2005 at 20:14:45 From: Daniela Subject: I need help with figuring out word problems I need help with figuring out word problems. I just don't understand them! I have this problem: You are taking part in a charity walk-a-thon where you can either walk or run. You walk at 4 km per hour and run 8 km per hour. The walk-a-thon lasts 3 hours. Money is raised based on the total distance you travel in 3 hours. Your sponsors donate $15 for each kilometer you travel. Write an expression that gives the total amount of money raised. Evaluate the expression if you walk for 2 hours and run for 1 hour. The most difficult part about problems like this is what do I do first? When I read the question, I don't understand what they are asking me and from there I give up. In this problem they ask me to find the expression, but I don't know how to set it up and I don't understand what is going to be my variable in the expression. Well, if I walk for 2 hours, then I must travel 8 km because I multiply 4 km/h by 2 hrs. Then, I did 8 km/h multiplied by 1 hour, and find that I will run 8 km. After that, I added the 8's together to find the whole distance and I got 16 km. Then, I took that 16 km and multiplied it by $15 to find the amount of money raised...I got $240. I'm pretty sure that this is the right answer, but now I don't know how to make it into an expression, so that when I substitute 2 hours and 1 hour for the variable I get $240.
Date: 09/02/2005 at 21:34:37 From: Doctor Peterson Subject: Re: I need help with figuring out word problems Hi, Daniela. A lot of students have trouble with word problems. Let's see what I can do for you. Probably the first thing to do is just to make sure you understand the problem--what is going on, and how are the various parts related? I like to write down the data in some orderly fashion, like this: Walk: 4 km/hr Run: 8 km/hr Time: 3 hr (total) Money earned: $15 per km Next, look for the unknown(s). What don't you know, that you would need to know in order to answer the question (in this case, how much money do you earn)? In the first part of the problem, you don't know how long you walked and how long you ran; you are asked to find an expression that will tell you what you earned IF you know these things. Now, we could either define TWO variables (for these two numbers), or we can notice that the two times are related by the fact that the total is 3 hr. If you walk 2 hr, you HAVE TO run 1 hr. So let's arbitrarily choose the time you walk as the unknown. (We could have chosen the running time instead.) Let w = time walked (in hours) I always state the unit used, because that saves a lot of trouble! Now, you've already done one of the things I like to suggest: walk through the calculation you'd do IF you knew the values. Since they gave you specific values to try, you tried them before making an expression. That's fine: it gives you a practice run before you actually start the algebra. So what did you do? You took the time walked and multiplied it by 4 to get the distance walked, and did the same with the time and distance run. Then you added those to get the total distance, and multiplied by 15 to get the money earned. Great job there! I'll put that down in an orderly way: time * speed = distance walking 2 hr 4 km/hr 2*4 = 8 km running 1 hr 8 km/hr 1*8 = 8 km total 16 km * $15/km = $240 Now all we have to do is to do just the same thing using variables. Remember that the walking time is w hours; the running time is what's left of the 3 total hours, or 3-w hours. time * speed = distance walking w hr 4 km/hr 4w km running 3-w hr 8 km/hr 8(3-w) km Do you see what I've done so far? I replaced your 2 hr and 1 hr with the expressions w and (3-w). Now I have to add those expressions, then multiply the product by 15. Can you finish, and write up the final expression? Once you've got that, try replacing w with 2 and see if you get 240. That will be a good check, besides answering the last part of the question. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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