1.A man travels 10km in 50mins if he runs for 8km and walks for 2km..if he runs 4km and walks 6km,his time is 1hr 15mins.find his running and walking speeds.
2.an equilateral triangle has has sides,,4acm,,3bcm,,and (a+b+c)cm,,,find a and b and the length of d sides of d triangle,,

Mods,,lalasticlala,,fp

Siimple simultaneous equations.

Simple simultaneous equations.

1. Running speed: 16km/hr
Walking speed: 6km/hr

skilfulsagei:
Simple simultaneous equations.

Oya solve na

ikihealthplus:
1.A man travels 10km in 50mins if he runs for 8km and walks for 2km..if he runs 4km and walks 6km,his time is 1hr 15mins.find his running and walking speeds.

Let r be his running speed and w be his walking speed.
Convert the times to hours
50 min = 50/60 = 0.833hrs
1 hr 15 min = 1 + (15/60) hr = 1.25 hrs
speed = distance/time
therefore, time = distance / speed

From the first statement, "A man travels 10km in 50mins if he runs for 8km and walks for 2km"
Expressing mathematically, we have (8/r) + (2/w) = 0.833........(i)

From the second statement, "if he runs 4km and walks 6km,his time is 1hr 15mins"
Expressing mathematically, we have (4/r) + (6/w) = 1.25....(ii)

Solving equations (i) and (ii) simultaneously, we have
r = 16 and w = 6.
Therefore running speed, r = 16 km/hr and walking speed, w = 6 km/hr.

ikihealthplus:

2.an equilateral triangle has has sides,,4acm,,3bcm,,and (a+b+c)cm,,,find a and b and the length of d sides of d triangle,,

try to arrange the dimensions properly, are they 4a cm, 3b cm and (a+b+c) cm??

vfactor:
1. Running speed: 16km/hr
Walking speed: 6km/hr

pls kindly show working

Drniyi4u:


Let r be his running speed and w be his walking speed.
Convert the times to hours
50 min = 50/60 = 0.833hrs
1 hr 15 min = 1 + (15/60) hr = 1.25 hrs
speed = distance/time
therefore, time = distance / speed

From the first statement, "A man travels 10km in 50mins if he runs for 8km and walks for 2km"
Expressing mathematically, we have (8/r) + (2/w) = 0.833........(i)

From the second statement, "if he runs 4km and walks 6km,his time is 1hr 15mins"
Expressing mathematically, we have (4/r) + (6/w) = 1.25....(ii)

Solving equations (i) and (ii) simultaneously, we have
r = 16 and w = 6.
Therefore running speed, r = 16 km/hr and walking speed, w = 6 km/hr.





try to arrange the dimensions properly, are they 4a cm, 3b cm and (a+b+c) cm??

yes they are,,,kudos to d 1st question

tried solving the first question simultaneously but couldn't get the answer....i got 24 as r and 10.67 as w...maybe i made a mistake somewhere or the process is wrong

for the second question,

4a=3b,...eq 1
a+b+c= 4a....eq2
form above, b+c=3a, therefore, 3b+3c= 9a...eq3, and 4a+3c=9a( substituting equation 1 in eq 3)
from above, 3c=5a...eq 4
finding a relationship between a, b and c in a one ration form,
3c=5a=(15b/4)....eq 5
which gives, 12c=20a=15b...eq 6
now we want to find independent ratios in the form of, a:c:b,
from above in eq 6,
a:c = 12: 20, c:b= 15:12...
therefore, a:c:b = 36:60:48.....which is 3:5:4....
making a=3, b=4, c=5....
QED!!!!!!!!!

now we want to find independent ratios in the form of, a:c:b,
from above in eq 6,
a:c = 12: 20, c:b= 15:12...
therefore, a:c:b = 36:60:48.....which is 3:5:4....
making a=3, b=4, c=5....
QED!!!!!!!!!
[/quote]kindly explain wat u mean by independent ratio,,i thnk u jst manipulated there,,coz taking ratio of a to c is 5 to 3 and not 3 to 5

ikihealthplus:
now we want to find independent ratios in the form of, a:c:b,
from above in eq 6,
a:c = 12: 20, c:b= 15:12...
therefore, a:c:b = 36:60:48.....which is 3:5:4....
making a=3, b=4, c=5....
QED!!!!!!!!!
kindly explain wat u mean by independent ratio,,i thnk u jst manipulated there,,coz taking ratio of a to c is 5 to 3 and not 3 to 5

if you dont understand, simply ask for further clarification! YOU don't tell me i manipulated!...

and by the way, to become better and faster in solving mathematics, you must be able to decipher lump steps even without writing it down....

Now let me explain to you step by step;

12c=20a=15b, is an embedded ratio...to make it independent means, to have the letters in one side and the figures at the other side, like,
x:y:z= 50:100:150......you get!

now since we have, 12c=20a=15b,
now, trying to make the ration in that form,
c/a=20/12, c:a=20:12,
c/b=15/12, c:b = 15:12,
rearranging, a:c= 12:20, c:b= 15:12,
now combine the two above into one,
we do that by making the value of c to be same, hence multiply the first by 3, then the second by 4,
which gives,
a:c= 36:60, and c:b = 60:48,
therefore, a:c:b = 36:60:48, equivalent to 3:5:4,
i.e., a=3, c=5, b=4.....

any confusion?

MoyoGENERAL:


if you dont understand, simply ask for further clarification! YOU don't tell me i manipulated!...

and by the way, to become better and faster in solving mathematics, you must be able to decipher lump steps even without writing it down....

Now let me explain to you step by step;

12c=20a=15b, is an embedded ratio...to make it independent means, to have the letters in one side and the figures at the other side, like,
x:y:z= 50:100:150......you get!

now since we have, 12c=20a=15b,
now, trying to make the ration in that form,
c/a=20/12, c:a=20:12,
c/b=15/12, c:b = 15:12,
rearranging, a:c= 12:20, c:b= 15:12,
now combine the two above into one,
we do that by making the value of c to be same, hence multiply the first by 3, then the second by 4,
which gives,
a:c= 36:60, and c:b = 60:48,
therefore, a:c:b = 36:60:48, equivalent to 3:5:4,
i.e., a=3, c=5, b=4.....

any confusion?

nice one bro

well done

MoyoGENERAL:


if you dont understand, simply ask for further clarification! YOU don't tell me i manipulated!...

and by the way, to become better and faster in solving mathematics, you must be able to decipher lump steps even without writing it down....

Now let me explain to you step by step;

12c=20a=15b, is an embedded ratio...to make it independent means, to have the letters in one side and the figures at the other side, like,
x:y:z= 50:100:150......you get!

now since we have, 12c=20a=15b,
now, trying to make the ration in that form,
c/a=20/12, c:a=20:12,
c/b=15/12, c:b = 15:12,
rearranging, a:c= 12:20, c:b= 15:12,
now combine the two above into one,
we do that by making the value of c to be same, hence multiply the first by 3, then the second by 4,
which gives,
a:c= 36:60, and c:b = 60:48,
therefore, a:c:b = 36:60:48, equivalent to 3:5:4,
i.e., a=3, c=5, b=4.....

any confusion?

oga,isn't an equilateral triangle supposed to have all 3 sides and angles equal?

so from ur calc 3,4 and 5..it isn't an equilateral triangle again...

dubylhover:


oga,isn't an equilateral triangle supposed to have all 3 sides and angles equal?

so from ur calc 3,4 and 5..it isn't an equilateral triangle again...

haba bros....check am well naa.
one side is 4a=4×3=12,
one is 3b=3×4=12,
and the last is =3+4+5=12...

look well ooo.

can any one help me out with this pls!!


y''-4y'+9y=t with y(0)=0 y'(0)=1

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