Answer:
Step-by-step explanation:
Fame age be x and sister's age = y
Five years ago:
Fame's age = x - 5
His sister's age = y -5
[tex]x -5 =\dfrac{1}{6}*(y-5)\\\\[/tex]
Multiply the entire equation by 6
[tex]6*(x-5)=6*\dfrac{1}{6}(y-5)\\[/tex]
6x- 6*5 = y-5
6x - 30 = y - 5
6x -30 + 5 = y
y = 6x - 25--------------(I)
Three year after:
Fame's age = x + 3
His sister's age = y + 3
2*(x +3) = y + 3
2x + 6 = y + 3
2x + 6 -3 = y
y = 2x + 3 -------------(II)
Substitute y = 6x - 25 in equation (II)
6x - 25 = 2x + 3
Add 25 to both sides
6x = 2x + 3 + 25
6x = 2x + 28
Subtract 2x from both sides
6x - 2x = 28
4x = 28
Divide both sides by 4
x = 28/4
x = 7
Substitute x = 7 in equation (I)
y =6x - 25
y = 6*7 - 25
= 42 - 25
y = 17
Fame's age = 7 years
His sister's age = 17 years
4) Let the distance between X and Y be D
Time take by Wie = distance÷ speed
[tex]= \dfrac{D}{75}[/tex]
Time taken by Wary = distance ÷ speed
[tex]=\dfrac{D}{80}[/tex]
Time difference = 10 minutes.
As Wary drives in high speed that Wie, he takes less time
[tex]\dfrac{D}{75}-\dfrac{D}{80}= \dfrac{10}{60}\\\\[/tex]
LcM = 1200
[tex]\dfrac{16D}{75*16}-\dfrac{15D}{85*15}=\dfrac{1}{6}\\\\\\\dfrac{16D-15D}{1200}=\dfrac{1}{6}\\\\\\\dfrac{D}{1200}=\dfrac{1}{6}\\\\\\D=\dfrac{1}{6}*1200\\\\\\[/tex]
D = 200 Km
