SOLUTION: If Alexandra increases her usual driving speed by 15 km/h, it will take her 2h less to make a trip to her grandparents' house. If she decreases her usual speed by 15 km/h, it will

Question 415092: If Alexandra increases her usual driving speed by 15 km/h, it will take her 2h less to make a trip to her grandparents' house. If she decreases her usual speed by 15 km/h, it will take her 3 h more than usual to make the trip. How long is the trip?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
If Alexandra increases her usual driving speed by 15 km/h, it will take her 2h less to make a trip to her grandparents' house. If she decreases her usual speed by 15 km/h, it will take her 3 h more than usual to make the trip. How long is the trip?

let usual speed = x mph
speed increased by 15km/h
speed = x+15 km/h
...
usual time = y
time with increased speed = y-2
xy = (x+15)(y-2)
xy=xy-2x+15y-30
2x-15y=-30.....................1
...
speed decreased by 15 km/h
time = y+3
..
xy = (x-15)(y+3)
xy=xy+3x-15y-45
3x+15y=-45....................2
2x-15y=-30.....................1
...
speed decreased by 15 km/h
time = y+3
..
xy = (x-15)(y+3)
xy=xy+3x-15y-45
3x+15y=-45....................2
2x-15y=-30.............1
-3x+15y =-45 .............2

multiply (1)by 1
Multiply (2) by 1
2x-15y =-30
-3x+15y =-45

Add the two equations
-1x=-75
/-1
x=75 km/h

plug value of x in (1) 2x-15y =-30
150-15y =-30
-15y =-30+-150
-15y=-180
y=12 hours
Distance = speed * time
Distance = 75*12= 900 km

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