word problems

[christina18]

Hello, I am new to this website. Can somebody please tell me how to begin these word problems? Thanks so much!

1. Kurt rows 72km upstream back in a total of 7 hours. the speed of the river is 3km/h. Find Kurt's speed in still water.
a) 21km/h
b) 24km/h
c) 18 km/h
d) 36 km/h


2. Working together, Carla and Elise can cut and split a cord of wood in 4 hours. Working alone, Carla takes 6 hour more than Elise. How long would it take Elise to do this job alone?
a) 12hr
b) 8hr
c) 6hr
d) 10hr

3. The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 180cm^3 under a pressure of 26 kg/cm^3. What will be its volume under a pressure of 80 kg/cm^3?
a) 514 cm^3
b) 63 cm^3
c) 12.4 cm^3
d) 98cm^3

 

[stapel]

1. Kurt rows 72km upstream back in a total of 7 hours. the speed of the river is 3km/h. Find Kurt's speed in still water.

Use the standard "uniform rate" formula, "d = rt":

. . . . .upstream:
. . . . .distance: 72
. . . . .rate: b - 3
. . . . .time: 72/(b - 3)

. . . . .downstream:
. . . . .distance: 72
. . . . .rate: b + 3
. . . . .time: 72/(b + 3)

Add their times. Set equal to the given total. Solve for the boat's speed.

2. Working together, Carla and Elise can cut and split a cord of wood in 4 hours. Working alone, Carla takes 6 hour more than Elise. How long would it take Elise to do this job alone?

Follow the standard procedure and convert the times to rates:

. . . . .hours to complete job:
. . . . .elise: e
. . . . .carla: e + 6
. . . . .together: 4

. . . . .completed per hour:
. . . . .elise: 1/e
. . . . .carla: ???
. . . . .together: 1/4

Complete the table. Add the individual efforts. Set equal to the total effort. Solve.

3. The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 180cm^3 under a pressure of 26 kg/cm^3. What will be its volume under a pressure of 80 kg/cm^3?

"Variation" exercises translate as follows:

. . . . ."y varies directly as x": y = kx
. . . . ."y varies inversely as x": y = k/x
. . . . ."y varies jointly as x and z": y = kxz

Translate your exercise into the appropriate form. Plug in the given numbers, and solve for the variation constant "k". Then start over again with the original form (but with the value plugged in for k), and find V and the given pressure P.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[TchrWill]

Hello, I am new to this website. Can somebody please tell me how to begin these word problems? Thanks so much!

Working together, Carla and Elise can cut and split a cord of wood in 4 hours. Working alone, Carla takes 6 hour more than Elise. How long would it take Elise to do this job alone?
a) 12hr
b) 8hr
c) 6hr
d) 10hr

Using another example:
1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

In your case, E(E + 6)/(E + E + 6) = 4
Simplifying, E^2 - 2E - 24 = 0
Use the quadratic equation to fnd E and then C.

 

[christina18]

Ok so for the 1st word problem...we have 2 times....
time: 72/(b - 3) and time: 72/(b + 3)

So how do I add their times. Set equal to the given total. Solve for the boat's speed. Do I do distributive property but divide? So for 72/(b - 3)= 72B-24?


For word problem number 2....how do I go about adding their individual efforts? I'm kinda lost on how and what to substitute in for those question marks?

For problem number 3, is the correct choice C?

 

[Denis]

Ok so for the 1st word problem...we have 2 times....
time: 72/(b - 3) and time: 72/(b + 3)

So how do I add their times. Set equal to the given total. Solve for the boat's speed. Do I do distributive property but divide? So for 72/(b - 3)= 72B-24?

HOW in heck do you get 72/(b - 3)= 72B-24?

The total time is 7 hours, so:

72 / (b - 3) + 72 / (b + 3) = 7

Solve that for b : start by multiplying each term by (b-3)(b+3);
you should end up with this quadratic: 7b^2 - 144b - 63 = 0

 

[christina18]

Stapel had told me how to start off the problems, that is where I tried to continue finishing up the rest...am I correct in the answers that I had chosen?

 

[Denis]

Stapel had told me how to start off the problems, that is where I tried to continue finishing up the rest...am I correct in the answers that I had chosen?

Look, Christina, you're confusing this to ne end... WHAT answers?

I suggest you start a new thread, AND BE CLEAR :evil:

 

[christina18]

Ok so for the 1st word problem...we have 2 times....
time: 72/(b - 3) and time: 72/(b + 3)

So how do I add their times. Set equal to the given total. Solve for the boat's speed. Do I do distributive property but divide? So for 72/(b - 3)= 72B-24?

For word problem number 2....how do I go about adding their individual efforts? I'm kinda lost on how and what to substitute in for those question marks?

For problem number 3, is the correct choice C?

 

[TchrQbic]

Ok so for the 1st word problem...we have 2 times....
time: 72/(b - 3) and time: 72/(b + 3)

So how do I add their times. Set equal to the given total. Solve for the boat's speed. Do I do distributive property but divide? So for 72/(b - 3)= 72B-24?


For word problem number 2....how do I go about adding their individual efforts? I'm kinda lost on how and what to substitute in for those question marks?

For problem number 3, is the correct choice C?

This isn't a new thread; it's a reply to the old one. Click on "new topic" and repost these questions (preferably only one or two at a time), and please make an attempt to work each problem. Several of the tutors have already given you hints that should be helpful. Then we can see where you need instruction or assistance.

 

[TchrWill]

Lets put these to rest

Hello, I am new to this website. Can somebody please tell me how to begin these word problems? Thanks so much!

1. Kurt rows 72km upstream back in a total of 7 hours. the speed of the river is 3km/h. Find Kurt's speed in still water.
a) 21km/h
b) 24km/h
c) 18 km/h
d) 36 km/h

1. Kurt rows 72km upstream back in a total of 7 hours. the speed of the river is 3km/h. Find Kurt's speed in still water.
a) 21km/h
b) 24km/h
c) 18 km/h
d) 36 km/h

I am assuming that the trip is 72km each way.
1--Let Kurt's speed be V
2--Then, 72/(V + 3) + 72/(V - 3) = 7
3--This reduces to 7V^2 - 144 - 63 - 0
4--By means of the quadratic equation, V = [144+/-sqrt(144^2 + 4(7)63)]/14
5--This reduces to V = (144+/-150)/14 = 294/14 = 21km/hr.


2. Working together, Carla and Elise can cut and split a cord of wood in 4 hours. Working alone, Carla takes 6 hour more than Elise. How long would it take Elise to do this job alone?
a) 12hr
b) 8hr
c) 6hr
d) 10hr

Using another example to derive a useful expression:
1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - The combined working time of two people can be derived from the expression Time = T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B. A and B are the individual working times to complete the job.

In your case, we have E and (E + 6) as trhe two speeds making E(E + 6)/(E + (E + 6)) = 4
Simplifying, E^2 - 2E - 24 = 0
Using the quadratic equation to fnd E we have
E = [+/-sqrt(2^2 + 4(24)}/2 = [2+/-10]/2 = 12/2 = 6 hrs.making Carla's working alone time 12 hrs.


3. The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 180cm^3 under a pressure of 26 kg/cm^3. What will be its volume under a pressure of 80 kg/cm^3?
a) 514 cm^3
b) 63 cm^3
c) 12.4 cm^3
d) 98cm^3

V....180
P.....26

If directly proportionl to pressure, the volume would be 180(80//26) = 553.8cm^3.

But inversely proportioal yields a voume of 180(26/80) = 58.5 cm^3.

This happens to be none of the answers you offered so either your list is incorrect or I am wrong, which is certainly possible.