Question

smith engineering found that an experienced surveyor surveys a roadbed in 4 hours. An apprentice surveyor needs 5 hours to survey the same stretch of road. If the two work together, find how long it takes them to complete the road.

Answer 1

Turn it into an equation. So the experienced guy works at a pace of 1/4 per hour and the apprentice works at a pace of 1/5 per hour. The equation then becomes\[\frac{ 1 }{ 4 }x + \frac{ 1 }{ 5 }x = 1\] Where x is the hours worked and 1 is one whole road. Then solve the equation.

Answer 2

Understand?

Answer 3

yes

Answer 4

would that equal 2/9x=1?

Answer 5

I don't know if you mistyped but it's actually 9/20x = 1
To solve this, isolate the x by multiplying both side by 20/9.

Answer 6

so x = 1*20/9

Answer 7

\[\frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } = \frac{ 5 }{ 20} + \frac{ 4 }{ 20 } = \frac{ 9 }{ 20 }\]

Answer 8

I'm confused on how that got to that.

Answer 9

which part? the 9/20?

Answer 10

the entire thing is just confusing to me. I apologize.

Answer 11

No it's fine. Do you get how I got the original equation:
1/4x +1/5x = 1

Answer 12

yes I understand that

Answer 13

Okay now add the fractions 1/4x +1/5x. You can ignore the x for now and just add the fractions.

Answer 14

1/20?

Answer 15

When you add fractions, you have to change the fractions so that they have the same denominator (bottom number). To change the fractions, you have to multiply the top and bottom by the same or you change the value of the equation.In this case:\[\frac{ 1 }{ 4 }\times \frac{ 5 }{ 5 } + \frac{ 1 }{ 5 }\times \frac{ 4 }{ 4 }\]

Answer 16

20 is the least common multiple of 4 and 5 (the smallest number that is a multiple of both 4 and 5) and you should change the denominator of both fractions to 20

Answer 17

To change a fraction without changing its value, you need to multiply the top and bottom of the fraction by the same number

Answer 18

Understand that part?

Answer 19

yes I understand that

Answer 20

Okay so now the fraction is 4/20 + 5/20 which is 9/20.
Hence the 9/20x = 1

Answer 21

Ok I got that part

Answer 22

Now the solve for x, you need to get rid of the 9/20. The best way to do this is to multiply the fraction by its reciprocal (the fraction flipped upside down) In this case it would be
9/20 * 20/9 That would just leave x because of cross-multiplication. But remember, what you do to one side of an equation, you have to do to the other. So the equation become
9/20x * 20/9 = 1 * 20/9

Answer 23

sorry not cross-multiplication. Ignore that part

Answer 24

ok so you multiply 1* 20/9?

Answer 25

yup which just 20/9

Answer 26

so x = 20/9. It will take them both 20/9 hours to finish the road.

Answer 27

oh alright well thank you for your help

Answer 28

hope you learned something. it's hard to explain through typing

Answer 29

I did thank you

Answer 30

you're welcome