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# System of equations word problem: walk & ride

Systems of equations can be used to solve many real-world problems. In this video, we solve a problem about distances walking and riding bus to school.

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• I get confused by this type of solution because of the units. It's funny how you can just have a system of equations despite all their different units. Like he sums one equation that deals with distance (km) and another that deals with time (hours). How is that not conflicting? This cause my brain to shut down a little... •  Maybe it's easier to see this when you make the times, rather than the distances, the unknowns.

If w is time walking and b is time busing, then

1) 5w + 60b = 35
[(5mph * w hrs) + (60mph * b hrs) = 35 miles (that is, speed1*time1 + speed2*time2 = total distance)]

2) 2w + 2b = 3
[from w + b = 1.5. (that is, time1 + time2 = total time)].

You can see here that while equation "1)" is about distance, and equation "2)" about time, that since the rates (5mph and 60mph) are not unknowns, they can be thought of simply as numbers that show another way that the two times are related, which gives you 2 (different) equations in two unknown times, which is enough information to get a solution.
• How did you get 11/12B by adding B and -B/12 together?
I don't get it at all! Please explain in an easier way.. • according to professionals from NASA and millions of researchers all across the globe:
We got B and add -B/12 or
B-B/12
which is equal to
1B-1B/12
look that the Bees have a legitimate exponent corresponding to one(1)
now:
1 is and can be 12/12 or any number over its number like 1/1
so:
12/12B-1B/12 and 1B/12 is 1/12B
so:
12/12B-1/12B
put bees aside and work out the fraction because everything we're working is with bees:
(12/12-1/12)B = 11/12 B
• I like to use substitution when solving problems with multiple equations. Is there a preferred method?
w = time walking, b = time riding the bus
w + b = 1.5, w = 1.5 - b, b = 1.5 - w
5w + 60b = 35 (speed times time equals distance)
5w + 60(1.5 - w)=35
5w + 90 - 60w = 35
5w - 60w + 90 - 90 = 35 - 90
-55w = -55
w = 1, b = 0.5
5(1) + 60(.5) = 35
5 + 30 = 35
The trip to school: 5 kilometers walked in an hour and 30 kilometers traveled on the bus in 0.5 hours. • I struggle when doing word problems in how to define my variables. I noticed in this video that Sal went straight to what question the problem was asking and defined his variables based on that. Is that a good idea in general to define your variables based on the question? • i don't get how you can subtract 1.5hours from 35 kilometers :( • Why does he put w over 5 and b over 60 into fractions? Is there other ways you where you don't have to have fractions to solve the linear equation? • Where did the 12 come from? Sounds like it should’ve been
5b/60.

5/60 is NOT 12. • Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 5 minutes total giving both instructions, and spoke 270 more words in Polish than in Hungarian.

This was very confusing how the problem gave the step by steps. I don't understand what made the y value a negative along with the constant after the equal symbol. the step by step wrote it as 150x-190y=-270, I thought it would be 150x+190y=270 And x+y=5 • Let P be time in Polish and H be time in Hungarian, so P + H = 5
I would have started the second equation as 190P = 150H + 270 (more than is + ). Thus it could be either 190P - 150H = 270 (this is the one that makes more sense to me) or 150H - 190P = -270 (this would work, but not what I would choose).
I would then multiply first times 150, 150P + 150P = 750, add two equations 340P = 1020, P = 3 so H = 2. Thus, 190(3) = 570 and 150(2) = 300 to check our second equation 570 = 300 + 270.
• Hi,
Do anyone know where in Khan Acadamy does it teach the elimination method? I got stuck on a question and when I click on the hints it told me to use that method, but I have never heard of it.  