Random maths help questions (1 Viewer)

[Fortian09]

A man walks from place A to place B at the speed of 3 km/h and cycles immediately to place A along the same road at a speed of 15km/h. Find the average speed for the whole trip.



If x^2+y^2=5 and x+y=3, find the value of x-y.




If 3a=2b=5c, find 1/a:1/b:1/c.


Thank you for your help
and if anyone wants to add homework questions to here please do

 

[lyounamu]

A man walks from place A to place B at the speed of 3 km/h and cycles immediately to place A along the same road at a speed of 15km/h. Find the average speed for the whole trip.

Let the road be xkm.
Time taken is
From A to B: x/3
From B to A: x/15

Total time: 6x/15
Distance is: 2x

The speed = distance/time
= 2x divided by 6x/15 = 5

If x^2+y^2=5 and x+y=3, find the value of x-y.

x = 3-y
x^2 + y^2 = (3-y)^2 + y^2 = 5
9 - 6y + y^2 + y^2 - 5 = 0
2y^2 - 6y + 4 = 0
y^2 -3y + 2 = 0
(y-2)(y-1) = 0
y = 2 or 1
x = 1 or 2

So x-y = 1-2 = -1 or x-y = 2-1 = 1

last question:

3a = 2b
a = 2b/3
1/a = 3/2b

5c = 2b
c = 2b/5
1/c = 5/2b

1/a : 1/b : 1/c = 3/2b : 1/b : 5/2b
= 3/2b : 2/2b : 5/2b
= 3/2 : 2/2 : 5/2 = 3:2:5

 

[3unitz]

If x^2+y^2=5 and x+y=3, find the value of x-y.

(x + y)^2 - 2xy = x^2 + y^2

3^2 - 2xy = 5

2xy = 4

(x - y)^2 = x^2 - 2xy + y^2

(x - y)^2 = 1

x - y = + 1

If 3a=2b=5c, find 1/a:1/b:1/c.

1/a : 1/(3a/2) : 1/(3a/5)

1/a : 2/3a : 5/3a

3 : 2 : 5

 

[Fortian09]

last question:

3a = 2b
a = 2b/3
1/a = 3/2b

5c = 2b
c = 2b/5
1/c = 5/2b

1/a : 1/b : 1/c = 3/2b : 1/b : 5/2b
= (3/2)/2b : 1/2b : (5/2)/2b
= 3/2 : 1/2 : 5/2 = 3:1:5

Hmm where did this come frome? (3/2)/2b : 1/2b : (5/2)/2b

 

[Fortian09]

but how does that get rid of the b?

 

[lyounamu]

but how does that get rid of the b?

I made a mistake there. I fixed it. Look it up to my edited one.

 

[Fortian09]

Thanks for the help