Help with Math problems (probably pretty easy for you guys)

[crhoody12]

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Hey everyone, I had a few (or seven) math problems I feel stupid that I can't do cause its been so long (now i'm making excuses). They've been collecting over the last month of my studying from a list I was making. If anyone can help, knows a hint, or easy way to do these problems and show me, I'd appreciate it. The problems are listed below with the answer the book gives in parenthesis. Thanks for all the help.

1.) .Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? (the answer is 15 minutes)

2.) ..If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? (the answer is 2m 44s)

3.) ..If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? (the answer is 1.09 days)

4.) A train traveled from Town A to Town B at an average speed of 48mph. The train returns from Town B to Town A along the same route at an average speed of 96mph. What was the average speed of the train, in mph, for the round trip? (book says 64mph)

5.) A committee of 2 people must be selected from a group of 16 people. In how many different ways may the committee be formed? (book says 120)

6.) There are 5 gold coins and 1 silver coin in a bag. If 2 coins are selected from this bag at random and without replacement, what is the probability that both coins are gold? (p = 2/3)

7.) Which of the following is 'x' equal to if y = (4x-5)/(3x+7)? [x = (7y+5)/(4-3y) ]
.

 

[Streetwolf]

Hey everyone, I had a few (or seven) math problems I feel stupid that I can't do cause its been so long (now i'm making excuses). They've been collecting over the last month of my studying from a list I was making. If anyone can help, knows a hint, or easy way to do these problems and show me, I'd appreciate it. The problems are listed below with the answer the book gives in parenthesis. Thanks for all the help.

1.) .Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? (the answer is 15 minutes)

2.) ..If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? (the answer is 2m 44s)

3.) ..If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? (the answer is 1.09 days)

4.) A train traveled from Town A to Town B at an average speed of 48mph. The train returns from Town B to Town A along the same route at an average speed of 96mph. What was the average speed of the train, in mph, for the round trip? (book says 64mph)

5.) A committee of 2 people must be selected from a group of 16 people. In how many different ways may the committee be formed? (book says 120)

6.) There are 5 gold coins and 1 silver coin in a bag. If 2 coins are selected from this bag at random and without replacement, what is the probability that both coins are gold? (p = 2/3)

7.) Which of the following is 'x' equal to if y = (4x-5)/(3x+7)? [x = (7y+5)/(4-3y) ]
.

#1, 2, and 3: you need the common rate per time. Take #2 for instance. Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes. You want to know how long it takes for 20 drinks. Steven mixes 4 drinks per minute, Sue mixes 2 drinks per minute, Jack mixes 4/3 drinks per minute. So they mix 22/3 drinks per minute. You want to know how long it takes to mix 20 drinks. So 22/3 drinks/minute * ?? minutes = 20 drinks. You get (3/22) * 20 = 30/11 = 2 and 8/11. Well 8/11 * 60 = 44 seconds so your answer is 2 minutes 44 seconds.

#4. A train traveled from Town A to Town B at an average speed of 48mph. The train returns from Town B to Town A along the same route at an average speed of 96mph. What was the average speed of the train, in mph, for the round trip?

Same distance, different times. Say the distance is 48 miles (easy!). Then it takes 1 hour to get there. So it takes 30 minutes to get back (why?). Total travel time is 1.5 hours. Total distance is 96 miles. You have 96/1.5 = 64 mph.

#5. A committee of 2 people must be selected from a group of 16 people. In how many different ways may the committee be formed?

Permutation. Simply put, we do (16 choose 2). This is because order does not matter. How many ways can we select 2 people? Well, we have 16 choices for person one and then 15 choices for person two. But it doesn't matter if we choose Matt then Paul or if we choose Paul then Matt. So how many ways can we order our subgroup? 2! ways (read: 2 factorial). Answer:

If you are choosing 'k' people out of a group of 'n' total people, the # of ways to do this WITHOUT regard to order is:

n! / ((n-k)! * k!)

For this, n = 16 and k = 2. We have 16! / ((16-2)!*2!) = 16!/(14! * 2!) = 16*15/2 = 8*15 = 120.


#6. There are 5 gold coins and 1 silver coin in a bag. If 2 coins are selected from this bag at random and without replacement, what is the probability that both coins are gold?

First coin: odds are 5/6. Second coin: odds are 4/5 (five coins left, four are gold). Multiply them, you get 2/3.

#7. Which of the following is 'x' equal to if y = (4x-5)/(3x+7)?

Cross multiply: y(3x+7) = 4x - 5
3xy + 7y = 4x - 5
4x - 3xy = 7y + 5
x(4 - 3y) = 7y + 5
x = (7y + 5) / (4 - 3y)

 

[BodybldgDoc]

1.) .Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? (the answer is 15 minutes)

Jim (T1)=30min
Sue(T2)=45min
Tony(T3)=1.5 hours=90min

Together, 1/T= 1/T1+1/T2+1/T3
= 1/30+1/45+1/90
=5(1/6+1/9+1/18)
=5(1/3)=1/15
1/T=1/15
T=15 min
.

 

[snapple59]

Hey everyone, I had a few (or seven) math problems I feel stupid that I can't do cause its been so long (now i'm making excuses). They've been collecting over the last month of my studying from a list I was making. If anyone can help, knows a hint, or easy way to do these problems and show me, I'd appreciate it. The problems are listed below with the answer the book gives in parenthesis. Thanks for all the help.

1.) .Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? (the answer is 15 minutes)

2.) ..If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? (the answer is 2m 44s)

3.) ..If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? (the answer is 1.09 days)

4.) A train traveled from Town A to Town B at an average speed of 48mph. The train returns from Town B to Town A along the same route at an average speed of 96mph. What was the average speed of the train, in mph, for the round trip? (book says 64mph)

5.) A committee of 2 people must be selected from a group of 16 people. In how many different ways may the committee be formed? (book says 120)

6.) There are 5 gold coins and 1 silver coin in a bag. If 2 coins are selected from this bag at random and without replacement, what is the probability that both coins are gold? (p = 2/3)

7.) Which of the following is 'x' equal to if y = (4x-5)/(3x+7)? [x = (7y+5)/(4-3y) ]
.

These are easy questions. 5th grade math 😀
1). 1/30 + 1/45 + 1/90 = 1/x --> 3/90 + 2/90 + 1/90 =1/x --> 6/90 = 1/x
6x= 90 x= 15 ----> 15 mins.

2). similar to 1st question. 20/5 + 20/10 + 20/15 = 20/x ---> 120/30 + 60/30 + 40/30 = 20/x ---> 220/30 = 20/x ---> 600=220x x=2.73

3). same as 1st question

4). Assume that the distance the train travel is 100 miles, and get the time for one way trip and return trip. Average speed= Distance/time

100 mi x hr/48mi = 2.083 hr 100 mi x hr/96 mi = 1.0417 hr

2.083 hr + 1.0417 hr = 3.125 hr

200 mi/3.125 hr = 64 mph

5). I hate probability question.

6). someone do 5 & 6 😀




7). y = (4x-5)/(3x+7) multiply both side by 3x+7 first
3xy+7y = 4x-5 subtract 3xy from both sides and add 5 from both sides
7y+5 = 4x-3xy divide x from the right hand side 7y+5 = x(4-3y)
and divide both sides by 4-3y
x= (7y+5)/(4-3y)