Rosemary, Leah and Josh walk a total distance of 42 kilometres to raise money for charity. Josh walks one-third of the distance and Leah walks one-quater of the distance.
a) How far does each person walk?
b) What fraction of the total distance does Rosemary walk?
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I don't need the answer. I'd just like to know as to weather i have the right method.
Do i multiply the distance, (that the people have walked) by the shown distance out of the 42 kilometres? what equation(s) would i use to solve (a) and (b)??
no, you wouldn't multiply. anyway, i misread the question originally, i didnt realize we were dealing with three people.
okay, remember i told you a while back that in math "of" means multiply. we will use that. now the total distance we are talking about is 42 km. Josh walks 1/3 of the distance, Leah walks 1/4 of that distance.
it probably makes more sense to find the fraction of the distance Rosemary walks first, but let's do it how the problem says we should.
(a) now we find the distance they each walk.
Josh:
Josh walks 1/3 of the distance, the total distance is 42, so the distance Josh walks is:
1/3 * 42 = 14 km
Leah:
Leah walks 1/4 of the distance, the total distance is 42, so the distance Leah walks is:
1/4 * 42 = 10.5 km
Rosemary:
The total distance the three walk add up to 42 km. let the distance Rosemary walks be x, then we must have:
x + 14 + 10.5 = 42
=> x = 42 - 14 - 10.5
=> x = 17.5 km
so Rosemary walks 17.5 km
Note that 17.5 = 35/2
(b) to find the fraction of the distance Rosemary walks we must put the distance she walks over the total distance. so the fraction of the distance she walks is:
(35/2)/42 = 35/2 * 1/42 = 5/12
Okay thanks but one thing:
quote: x + 14 + 10.5 = 42
=> x = 42 - 14 - 10.5
=> x = 17.5 km
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The x that represents rosemarys distance. When were doing the sum : x + 14 + 10.5 = 42
when were actually doing it on the calculator, would we leave the x, and go onto 14 + 10.5 - 42? or i do exactly what i just said only without clearing the result i'd go onto 42 - 14 - 10.5??
Sorry i'm a bit lost.
we begin by setting up the equation:
x + 14 + 10.5 = 42 ..............you understand how we got there right?
now we subtract 14 and 10.5 from both sides, not on a calculator, we just rewrite:
x = 42 - 14 - 10.5
now we enter the right side into our calculator to find what x is, or we can do it by hand
i'm not sure i understand your question. our objective is to find how much the x represents, if we knew it before hand, there would be no point in calculating it. i just set up that equation because i know all the distances walked by the three add up to 42. I know Josh walked 14 and Leah walked 10.5 i do not know how far Rosemary walked, so I called that x. Then i try to find x by solving the equation
Hello,
it seems to me that you have some difficulties to imagine what is going on behind those equations. If so, then draw a rough sketch (see attachment).
As you can see, you'll get the distance which was walked by Rosemary if you "cut off" the two other distances. That means:
Rosemary's distance = 42 km - 14 km - 10.5 km
The length of the red arrow correspond to the distance which was walked by Rosemary.