Respuesta :
Answer:
Therefore,
Distance of the trip is
[tex]Distance =900\ km[/tex]
Step-by-step explanation:
Let "x" be the Speed of the car and,
"y" be the time to cover the trip to her grandparents,
To Find:
How long is the trip = ?
Solution:
We Know that,
[tex]Distance = Speed\times Time[/tex]
According to the First given condition,
[tex]Speed = x + 15[/tex]
[tex]Time = y - 2[/tex]
According to the Second given condition,
[tex]Speed = x - 15[/tex]
[tex]Time = y + 3[/tex]
As we know Distance will remain same so we have
[tex]Distance = Speed\times Time= x\times y[/tex]
Substituting the values we get
[tex](x+15)\times (y-2)=(x-15)\times (y+3)=x\times y[/tex]
So on Substituting we have
[tex](x+15)\times (y-2)=(x-15)\times (y+3)[/tex]
[tex]5x-30y=15\\Divding\ by\ 3\\x-6y=3[/tex]..............Equation ( 1)
Again on Substituting we have
[tex](x-15)\times (y+3)=x\times y[/tex]
[tex]3x-15y=45\\Dividing\ by\ 5\\x-5y=15[/tex]...........Equation ( 2)
Subtracting Equation 1 from equation 2 we get
[tex]x- x -5y--6y=15-3\\\\y=12[/tex]
Substitute y = 12 in equation 1 we get
[tex]x-6\times 12=3\\x = 72+3=75[/tex]
So we have now,
[tex]Speed = 75\ km/h[/tex]
[tex]Time = 12\ h[/tex]
Therefore the Distance of the trip is
[tex]Distance = x\times y=75\times 12=900\ km[/tex]
Therefore,
Distance of the trip is
[tex]Distance =900\ km[/tex]
