Algebra 1 Word Problems - DRT
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Way To Go
Word Problems - DRT

 
 You drive down the road at 55 miles per hour for 2 hours.
 
 How far did you go?
 
 Some people can do this one in their heads.
 
 The answer is 110 miles.
 
 The actual formula for doing problems like this one is ...
 

 

 
 So for the problem we started with ...
 
 Speed you were going = 55 mph
 Time you were traveling = 2 hours
 Distance traveled = ? (what we need to find out)
 
 So:

 Distance Traveled = 55 2 = 110

 
 Remember the page on percents?
 We said that percent was the combination of per
 (meaning divided by)
 and cent (meaning 100).
 
 Here, when we say 55 miles per hour
 the per means the same thing, divided by.
 So 55 miles per hour actually means 
 "55 miles divided by one hour."
 

 

 
 In the problem we multiplied this by 2 hours.
 What we were actually doing was:
 

 
 Hey, this one looks like one of those
 unit conversion things!
 
 Well, that's part of what's going on here.
 We cancel the hours in the numerator
 with the hours in the denominator.
 

 
 We don't need to write in a denominator of 1
 so we can lose it ...
 

 
 The moral of he story is this.
 If the problem said
 "You were going 55 miles per hour for 20 minutes,"
 you would have to convert the 20 minutes 
 to whatever that is in hours before you could do the problem.
 
 Here's a picky point.
 Generally in these problems, they don't use the word speed.
 Instead, they use the word rate.
 Just remember that rate means speed.
 It's a thesaurus thing I guess.
 
 Example:
 
 You drive down the highway at 65 miles per hour for 20 minutes.
 How far IN FEET did you go?
 
 OK, OK, they want the answer in feet.
 That's no big deal.
 Somewhere along the line in the problem, 
 we need to convert our measures to feet.
 
 We could work the whole problem in miles if we want
 and then convert to feet at the end.
 
 We could also change 65 miles per hour 
 to whatever that is in feet per hour to begin with
 and then work the problem with that.
 Do whatever is easier for you.
 It doesn't matter.
 If you do the math right, you'll get the right answer.
 
 Distance = (What you want to find out)
 Rate (means speed) = 65 miles per hour
 Time = 20 minutes
 

 
 So we've got hours and minutes in the same problem.
 One of them needs to be changed 
 to be the same units as the other.
 The easiest way is to change 20 minutes
 to some amount of hours.
 
 Remember how we do it?
 

 

 
 So now we can do the problem ...
 

 

 
 The little line over the 66 means that this number
 (the 6's) repeat forever.
 
 So now we just need to change miles to feet.
 

 
 Let's do another one ...
 
 Example:
 
 We drive for 4 hours and go 190 miles.
 What was our average speed?
 
 We might not have been going the same speed
 for the whole 4 hours, 
 so we want the average speed for this time ...
 

Distance Traveled = Rate Time

 
 Distance = 190 miles
 Rate = (We don't know)
 Time = 4 hours
 
 So ...

190 miles = Rate 4 hours

 
 Let's use R to stand for rate and solve the problem for it.
 The math works just the same with an R
 as it does with an X ...

 

190 miles = Rate x 4 hours

 
 Divide both sides by 4 hours and simplify ...
 

 
 The rate (speed) was 47.5 miles per hour.
 
 OK, one last one ...
 
 Example:
 
 Two trains start at the same point.
 One train travels east at 40 miles per hour for at least 4 hours..
 The other train travels west at an unknown speed.
 4 hours later, the trains are 360 miles apart.
 What was the average speed of the second train.
 
 
 OK, now we have 2 moving objects.
 The distance we are given is the total distance they went together
 (Since they were traveling in opposite directions).
 
 We have:
 

360 = Distance traveled by train 1 + Distance traveled by train 2

 
 We know that:

 Distance Traveled = Rate Time

 
 So;

360 = Rate of train 1 Time + Rate of train 2 Time

 
 And we know:
 
 Rate of train 1 = 40 miles per hour
 Rate of train 2 = we don't know; call it R
 Time (for both) = 4 hours
 
 So we have:

 
 The rate of the second train is 50 miles per hour.
 

   copyright 2005 Bruce Kirkpatrick

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