Question

Two mechanics worked on a car. The first mechanic worked for hours, and the second mechanic worked for hours. Together they charged a total of . What was the rate charged per hour by each mechanic if the sum of the two rates was per hour?

Answer 1

Your question seems to be missing numbers..? Or is it just me?

Answer 2

yes it is missing numbers

Answer 3

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1800 . What was the rate charged per hour by each mechanic if the sum of the two rates was 155 per hour?

Answer 4

(1800 and 155) dolars

Answer 5

@Ashleyisakitty @whpalmer4

Answer 6

let's call the mechanics Fred and Sue. Fred's rate will be \(f\) and Sue's rate will be \(s\)
\[f+s = 155\]because the total rate is $155/hr.

Good so far?

Answer 7

yeah sure

Answer 8

Now Fred worked 10 hours and Sue worked 15, so the amount billed by Fred is how much?

Answer 9

remember, \(f\) is Fred's hourly rate

Answer 10

@whpalmer4 is it: f = 150 -s

Answer 11

No, Fred works 10 hours, at a rate of \(f\) per hour. For 10 hours work, he bills \(10f\), right?

Answer 12

and the other one 15s

Answer 13

Similarly, Sue bills \(15s\) for working 15 hours.

Right!

So can you write an equation that shows how they get to $1800 for the total bill?

Answer 14

so the systme would be:

10f + 15s =1800
f +s = 150

Answer 15

Close, but not quite. Look again at the sum of the two rates...

Answer 16

I cannot fail this question ! please

Answer 17

Hey, if you get it wrong with my help, I'll be very surprised :-)

Answer 18

oh yeah its is 155 in the secon equation

Answer 19

lol yeah i know you're a guru on math

Answer 20

with story problems my specialty :-)

Answer 21

are you solving by substitution or elimination?

Answer 22

would you like me to stop you now, or after you've calculated the other half of the wrong answer? :-)

Answer 23

\[10f+15s = 1800\]\[(-10)*f+(-10)*s = (-10)*155\]\[-10f -10s = -1550\]

Why don't you try using that as your second equation...

Answer 24

i see more clear now
lol

Answer 25

you know that if Sue doesn't charge anything for her time, then Fred charges 155/hr. Any answers that have someone making more than 155 are clearly wrong :-)

Answer 26

s = 50

Answer 27

get the other one too

Answer 28

what did I just say?

Answer 29

ok again i failed for do thigns too fast

Answer 30

100

Answer 31

plug those into original formulas, does the answer make sense?

Answer 32

for the first one it doesn't

Answer 33

okay, that means it isn't correct. maybe try with substitution instead?

Answer 34

ok

Answer 35

how are we doing?

Answer 36

well i was on determinants by ithinkj i failed again

Answer 37

okay, let's go through the solution both with substitution and elimination.

\[10f + 15s = 1800\]\[f+s = 155\]Agreed? Check your problem carefully, I don't want to be blamed for doing the wrong problem :-)

Answer 38

Fred works 10 hours, Sue works 15, they bill at a combined rate of $155, and the bill is $1800.

Answer 39

10(-s +155) +15s = 1800

Answer 40

Okay, good... keep going

Answer 41

5s = 250 --> 50

Answer 42

ok something is right. s!

Answer 43

Okay, what is Fred's rate if Sue's rate is 50?

Answer 44

f =1050/10

Answer 45

or 105

Answer 46

Plug both into the original equations (both of them). Do you get true statements from those answers? Remember, it must satisfy all of the equations to be correct.

Answer 47

yeah now it is right for the first one and the second one

Answer 48

oh man thanks a lot, You have been very helpful, are you a professor ?

Answer 49

10(105) + 15(50) = 1800
105 + 50 = 155

both true

Answer 50

Okay, let's do it by elimination:

\[10f + 15s = 1800\]\[f+s = 155\]I'm going to multiply the second one by -10

\[10f+15s = 1800\]\[-10f-10s=-1550\]
Agreed?

Answer 51

why don't you finish it off...

Answer 52

ok i will

Answer 53

0 + 5s = 250 --> 50

Answer 54

1) 10f +15(50) = 1800

10 f = 1800 -750

f = 1050/10 --> 105

Answer 55

I got excited earlier when you got s=50, but then it got away from you somehow. You should go back and look at what you did and try to understand what the mistake was, and why you made it. Learn from your mistakes! For example, I know that subtracting negative quantities is something that has a much higher chance of error when I do it, so I try to arrange my work to do less of that (and check it very carefully) when possible.

Answer 56

(f,s) --> (105,50)

Answer 57

brother seriously I'm so thankful, I'm going to verify with the determinants too cause any method has to work out

Answer 58

ah, you know the matrix route, too? good! I don't do it often enough to be confident in my abilities...

Answer 59

lol is long but i like it

Answer 60

you could also do this in your head via a different route :-)

assume that fred bills at the whole $155/hr. he works 10 hours, so that makes only $1550. That's $250 shy of the total bill. Now, Sue works 15 hours, so every dollar she bills adds 15 to the total, but 10 comes off the total because Fred doesn't bill that dollar, so giving a dollar/hour to Sue increases the take by a total of $5. You need to boost the take by $250, divided by $5/(dollar/hour) for Sue gives you a rate of 50/hour for Sue.
Easy, right?

Answer 61

amazing, i never thought that

Answer 62

what if i asume the oppsite, i mean starting with sue

Answer 63

i would have the f, right ?

Answer 64

That works too. She bills 15 hours, so that's 15*155 = 2325 (a bit harder to compute, that's why I did the other one!). That's 2325-1800 = 525 too high. Now the same calculation applies: every $/hour taken away from Sue cuts the total by $5, so what is $525/5? 105...

Answer 65

mmm i see,

Answer 66

with determinants it seems is impossible but anyway

Answer 67

if you want to really solidify your story problem skills, there's a good book called How to Solve Word Problems in Algebra by Mildred Johnson. she breaks down the dozen or so basic problem types (coins, mixtures, rates, etc.) and really does a good job of it, I think. See if you local library has a copy, or pick up a copy at the bookstore, it's an inexpensive paperback as I recall.

Answer 68

ok bro I will search that book , maybe it is on internet

Answer 69

see you the next time, bye