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ahrayia [7]
2 years ago
15

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 hous

e. 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?
Mathematics
1 answer:
Hitman42 [59]2 years ago
7 0

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

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