SOLUTION: Your help is appriciated.
I have worked 12 hours on this problem.
To get to his parent's house, John travels 60mph on land and then uses a motor boat that travels at a speed of
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Question 414260: Your help is appriciated.
I have worked 12 hours on this problem.
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?
The answer given is 138 miles. I am at a loss on how to solve this problem.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
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
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