SOLUTION: 1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28

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Question 388072: 1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28 boxes. find the total number of matches ?
2.mr. ong makes regular business trips to kaulalumpur a distance of 420 km from singapore (a)on his way up to kaulalumpur he travels along the trunk road at an average speed of x km/h. write down the expression in trm of x for the time taken in hours to travel from singapore to kaulalumpur
(b)on his return journey to singapore he travels along the north south highway and increases the average speed by 15 km/h.write down the expression in term of x for the time taken in the hours to travel from kaulalumpur to singapore.
(c)if the time difference between the two journey is 40 min from an equation in x and show that it reduces x^2+15x-9540=0
(d)solve the equation and find the time taken for the trip from singapore to kaulalampur
3.mr. kumar lives in the eastern part of the singapore. he visits his aged parents who lives 36 km away, evry weekends. he finds that if he increases the average speed of his vehicle by 12 km/h.he could save 9 min of his travelling time. find the speed at which he travels before the increase in speed.
Answer by mananth(16946) (Show Source):
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1.a certain number of matches are needed to fill 24 boxes with each boxes containing the same number of matches .when 4 less matches are put in to each box, there are enough for 28 boxes. find the total number of matches ?
let total match sticks be x
each box will contain x/24
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x/((x/24)-4)=28
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x/((x-96)/4)=28
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x*4/(x-96)=28
4x=28(x-96)
4x=28x-2688
24x=2688
/24
x=2688/24
match sticks
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2.mr. ong makes regular business trips to kaulalumpur a distance of 420 km from singapore (a)on his way up to kaulalumpur he travels along the trunk road at an average speed of x km/h. write down the expression in trm of x for the time taken in hours to travel from singapore to kaulalumpur
(b)on his return journey to singapore he travels along the north south highway and increases the average speed by 15 km/h.write down the expression in term of x for the time taken in the hours to travel from kaulalumpur to singapore.
(c)if the time difference between the two journey is 40 min from an equation in x and show that it reduces x^2+15x-9540=0
(d)solve the equation and find the time taken for the trip from singapore to kaulalampur
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FORWARD
speed x km/h
distance = 420 km
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t=d/r
t= 420/x hours
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RETURN
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speed = x+15 km/h
distance = 420 km
..
time = 420/(x+15) hours.
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40 minutes = 40/60 = 2/3
time going - time returning = 2/3 hours
(420/x)-420/(x+15)=3/4
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LCD = x(x+15)
multiply equation by x(x+15)
420(x+15)-420x=2/3* x(x+15)
420x+6300-420x=2/3*x(x+15)
6300=2/3*x(x+15)
multiply by3
18900=2x^2+30x
2x^2+30x-18,900=0
/2

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x^2+15x-9450=0
x^2+105x-90x-9450=0
x(x+105)-90(x+105)=0
(x+105)(x-90)=0
x= 90 km/h
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distance = 420 km
speed = 90 km/h
time = 420/90
hours Time to Kaula lumpur
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m.ananth@hotmail.ca
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3.mr. kumar lives in the eastern part of the singapore. he visits his aged parents who lives 36 km away, evry weekends. he finds that if he increases the average speed of his vehicle by 12 km/h.he could save 9 min of his travelling time. find the speed at which he travels before the increase in speed.
...
let his speed be x kmph
distance = 36 km
time = 36/x hours
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speed = x+12
distance = 36
time = 36/(x+12)
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36/x-36/(x+12)=9/60
(36(x+12)-36x)/(x(x+12)=3/20
(36x+432-36x)/x(x+12)=3/20
432=3x(x+12)/20
20*432=3x(x+12)
8640=3x^2+36x
/3
2880=x^2+12x
x^2+12x-2880=0
x^2+60x-48x-2880=0
x(x+60)-48(x+60)=0
(x+60)(x-48)=0Take the positive value for speed
km/h. Original speed
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m.ananth@hotmail.ca