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At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Let  H  be the number  of hours  that  train B travels

And the number of hours that train A travels = 2.5 + H

And   Rate * Time  = Distance Traveled

And when B catches A they will have traveled the same distance....so.....

100 (2.5 + H)  = 150 (H)    simplify

250 + 100H  = 150H          subtract 100H from both 

250  = 50H             divide both sides by  50

5   = H

So.....train B catches A at  4:30 PM + 5 hrs  =    9:30 PM

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Train A has a 2  1/2 hour head start     2 1/2 hr  x 100 mph = 250 m   head start

Train B travels (150 - 100) m/hr =   50 m/hr faster

   Start by finding how long it will take train B to cover the 250 mile gap at 50 m/hr

        now you will know how long train B has been travelling when it catches train A  

              then  rate   x  time  = distance from station

                   150 m/r    x time = distance

You should at LEAST try to solve ALL of these before postin all of your homework.....If you cannot even attemp them, you are in a clas too far advanced for your knowledge level and should be getting some remedial education.....

   THIS FORUM IS NOT FOR DOING YOUR HOMEWORK FOR YOU......sTOP BEING LAZY.   AT LEAST TRY !       THEN POST YOUR q'S

A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

Let x be the equal number of apples and pears....so

x - 1         2

____  =   ___              cross-multiply

x  - 5        1

1 ( x - 1)  = 2 ( x - 5)    simplify

x - 1 =  2x  - 10        add 10 to both sides, subtract x from both  sides

9  = x

The number of remaining pears =   x - 1  =  9  - 1   =  8

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

Let  x  be the number of chickens

Then 40 - x  =  the number of pigs

So

Legs per chicken * number of chickens  +  Legs per p*g * number of pigs  =  100

2x + 4(40 - x)  =  100   simplify

-2x + 160  = 100       subtract 160 from both sides

-2x = -60         divide both sides by -2

x = 30  = number of chickens

A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?

We have   that  A  can do (1/14)  of the work in one day

And A and B  can do (1/10)  of the work each day

Let (1/x) be the fraction of the work that B can do in one day

So

(1/14)  +  1 / x =  1/10         subtract   1/14  from both sides

(1/10)  - (1/14) =  1/x

[14 - 10 ] / 140  =  1/x

4 / 140  =  1/x      and we can write

140 / 4  =  x

35   = x

So....it takes B 35 days to do the work alone

Thanks, Noobfromvn  !!!

See detailed solution to your FIRST question here:  https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1076461.html

I also need help on these problems:

A can do a work in 14 days and working together A and B can do the same work in 10 days. In what time can B alone do the work?

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

A health club charges a one-time initiation fee and a monthly fee. John paid 100 dollars for 2 months of membership. However, Peter paid 200 for 6 months of membership. How much will Sylvia pay for 1 year of membership?

The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that show how many times a week Madison eats breakfast.

A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

8 / 2 * (2+2) = 8 / 2 * 4 = 4 * 4 = 16 ?

maybe just set this function equal to 6 and solve for t, the result will be two cases.

t1 nearly equal 0.57s

t2 nearly equal 2.29s

hope it can help :)

Hello guest! Agreed.  I should've added a word  reality  

What about this:       sqrt( |-25| ) = sqrt ( 25 )  

We can use a constructive approach, which isolates the unique probabilities for each card.  This gives us an answer of (1/16*c(16,1) + 1/15*c(16,2) + 1/14*c(16,3) + 1/13*c(16,4))/c(16,4) = 27/260.

solve this equation : (93+70+99+95+x) / 5 = 90

=> x = 93.

So that She must get at least 93 for reach an A :) Hope it can help

Are we assuming 'a' and 'k' are being multiplied by one? I'm sorry, I've gotten a little lost now. 

---------------------------

Melody's response.

a and k are just constants.  They are numbers, you just don't know what that number is.

You have to treat them just like you would treat a number.

Like

You should now kow that y=6 is a vertical line where the y values of all the points are 6.

Note

3 * 4 seaters   +  4 * 9 seaters  =

12 +  36  =

48

Lateral  surface area  =  

pi  * radius * slant height of cone

So

12√34 * pi  = pi * 6 * slant height of cone    [ divide out pi ]

12√34 =  6 * slant height of cone    [divide both sides by 6 ]

2√34 =  slant height of  cone  =   √ [ 34 * 4 ]  =  √ 136

Using the  Pythagorean Theorem......the height of the cone  =

√[ (√136)^2  -6^2 ]  = √ [136 - 36 ] =  √100  =  10

So.....the volume of the cone is

(1/3) pi * radius^2 * height  =

(1/3) pi (6)^2 * 10  =

(1/3) pi * 360  =

120 pi     units^3

This isn't really math...

m=m, in case you were wondering

The following outcomes  are  prime

2, 3, 5, 7, 11

Ways to roll    2    =  1

Ways to roll  3    =   2

Ways to roll  5  =  4

Ways to roll  7  =  6

Ways to roll 11 =  2

P ( 5  given that the outcome is a prime)  =

           4                                  4

______________  =            _____

1 + 2 + 4 + 6 + 2                   15

Yes

P ( first card is a club)   means  the probability of the first card being a club

Sorry I didn't make that clearer  !!!!

Also, when you say P ( first card is clubs) does that mean the probability of the first card being clubs?

Thanks!

Thank you!

P ( first card is clubs  ) =  13/52  =  1/4

P ( second is hearts)  =  13/51  

P( third is also clubs)  =   12/50  = 6/25

So....the total probability is

1/4  *  13/51 * 6 /25   =   78  / 5100   =    13 / 850