Word problems?

Question

Three pounds of walnuts cost $7.14. At this rate, how much would six pounds of walnuts cost? ( this one seems to easy, in my opinion the answer would be 14.28, is this correct)



A roofer requires 18 hours to shingle a roof. An apprentice roofer can do the job in 24 hours. How long would it take to shingle the roof if they work together?




A commercial jet travels 1560 mi. in the same amount of time it takes a corporate jet to travel 1200 mi. The rate of the commercial jet is 120 mi/h greater than the rate of the corporate jet. Find the rate of the corporate jet.

Answer 1

1. The answer of 14.28 is correct.

2. 18 hours=1 roof
24 hours=1 roof
h/18 hours +h/24 hours=1 roof
4h/72+3h/72=1
7h/72=1
7h=72
h=72/7 hours
h=10 2/7 hours
h=10.285714285714285714285714285714 hours


3. x=corporate jet rate; h=hours
1560=(120 mi/h+x mi/h)h
1200=xh
1560=120h+xh
since 1200=xh, then substitute 1200 for xh ==>
1560=120h+1200
360=120h
h=3
1200/3=400
120+400=520mi/h

Answer 2

1. Just multiply. 6 pounds are twice as many as 3 pounds, so its cost will be twice as much as the cost of 3 pounds.

2 x $7.14 = $14.28

2. Add their work rates, then solve for the time it will take them to complete one roof working together.

1st worker = 1 roof / 18 hours
2nd worker = 1 roof / 24 hours

together:
1 roof / 18 hours + 1 roof / 24 hours = 1 roof / x hours

(24 + 18) roofs / (24)(18) hours = 1 roof / x hours

42 roofs / 432 hours = 1 roof / x hours

Here we can cross-multiply:

42 roofs (x hours) = 432 hours (1 roof)
x hours = [432 hours (1 roof)] / 42 roofs
x hours = (432/42) hours
x hours = (72/7) hours
x hours ~ 10.29 hours

So it would take them approximately 10.29 hours, which is about10 hours and 17 minutes, if they worked together.

3. Their speeds are directly proportional to the distance they cover in the same amount of time. If we let D = the distance covered by the commercial jet and use the distance formula, D = RT, then 1560 = RT. Similarly, if we let D' be the distance covered by the corporate jet, then D' = 1200 = R'T', but since T = T', we can substitute that in for T'. Now we can set up a ratio, and T falls out of the equation entirely, allowing us to solve for R' in terms of R.

1560 / 1200 = RT / R'T = R / R'

Cross-multiplying, 1560R' = 1200R -----> R' = (1200 / 1560)R.

We are given that R = R' + 120. So we can substitute R' + 120 in for R. Then R' = (1200 / 1560)R becomes:

R' = (1200 / 1560)(R' + 120).

Now we manipulate the above equation algebraically to solve for R'.

R' = (1200 / 1560)(R') + (1200 / 1560)(120)
R' = (12 / 15.6)(R') + (12 / 15.6)(120)
R' = (12 / 15.6)(R') + (1440 / 15.6)
R' - (12 / 15.6)(R') = (1440 / 15.6)
(3.6 /15.6)R' = (1440 / 15.6)
R' = (1440 / 15.6) / (3.6 /15.6)
R' = (1440 / 3.6)
R' = 400 mph

The speed of the corporate jet then is 400 mph and the speed of the commercial jet is 400 + 120 = 520 mph. Now let's check these.

To travel 1200 miles, the corporate jet must travel 3 hours. If we let T' = T = 3 hours, then D' = 1200 miles and D = (3)(520) = 1560 miles, which are the distances originally specified in the problem, so we have the right answers.

Answer 3

Walnuts is right. Roofers: find how much each gets done in an hour; add, then make a proportion to equal 1 whole job:

1/18 + 1/24 = 4/72 + 3/72 = 7/72 total per hour

7/72 job in 1 hr = 1 job in x hrs

7/72x = 1; x = 72/7 hrs

Jets: the faster one went (1560 - 1200) = 360 more miles; see how long that would take at 120 mph

Answer 4

Question 1: Your answer is correct (14.28)

Question 2: I'm really sorry but I don't know..

Question 3: Why was the first one soo easy!

Answer 5

Walnuts, your answer is correct.
Roofers, I get 21 hours.
The jet one, I have no idea and am too lazy to figure it out!!! ; D