Question

if alexandra increases her usual driving speed by 15 km/h, it will take her 2 hours less to make a trip to her gradnparents house. If she decreaseshe rusualy speed by 15 km/h, it will take her 3 h more than usualy to make the trip. How long is the trip?

Answer 1

Answer:

Therefore,

Distance of the trip is

$Distance =900\ km$

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,

$Distance = Speed\times Time$

According to the First given condition,

$Speed = x + 15$

$Time = y - 2$

According to the Second given condition,

$Speed = x - 15$

$Time = y + 3$

As we  know Distance will remain same so we have

$Distance = Speed\times Time= x\times y$

Substituting the values we get

$(x+15)\times (y-2)=(x-15)\times (y+3)=x\times y$

So on  Substituting we have

$(x+15)\times (y-2)=(x-15)\times (y+3)$

$5x-30y=15\\Divding\ by\ 3\\x-6y=3$..............Equation ( 1)

Again on  Substituting we have

$(x-15)\times (y+3)=x\times y$

$3x-15y=45\\Dividing\ by\ 5\\x-5y=15$...........Equation ( 2)

Subtracting Equation 1 from equation 2 we get

$x- x -5y--6y=15-3\\\\y=12$

Substitute y = 12 in equation 1 we get

$x-6\times 12=3\\x = 72+3=75$

So we have now,

$Speed = 75\ km/h$

$Time = 12\ h$

Therefore the Distance of the trip is

$Distance = x\times y=75\times 12=900\ km$

Therefore,

Distance of the trip is

$Distance =900\ km$