Question 414260
To get to his parent's house, John travels 60mph on land and then uses a motor boat that travels at a speed of 20mph in still water. John goes by land to a dock and then travels on a river against acurrent of 4mph. He reches hs parent's home in 4.5 hours. The return trip takes 3.5 hrs. How far does his parents live from John's house? 


John land speed = 60 mph
let distance on land be x
water speed = 20 mph
let distance on water be y

time on land + timeon  water = total time
t= d/r
GOING
x/60+y/16 = 4.5 
LCD = 60*16
multily by 60*16
16x+60y =4.5 * 60*16
16x+60y=4320.................1

RETURNING
x/60+y/24 = 3.5
24x+60y=24*60*3.5
24x+60y=5040...................2 
.....


multiply (1)by 					-1			
Multiply (2) by					1			
-16x-60	y=-4320		
24x+60y=	5040		
								
Add the two equations							                                                                       8x=720		
								
/8							
								
x=90						
								
plug value of x in (1)								
								
16x+60y	=4320		
1440+60y	=4320		
60y=4320	-1440
60y=2880		
y=48		
Total distance = 90+48=138 miles