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?


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