SOLUTION: To get to his parents' house, John must travel at a speed of 60 mph on land and then use a motorboat that travels at a speed of 20 mph in still water. John goes by land to a dock a
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Question 1157574: To get to his parents' house, John must travel at a speed of 60 mph on land and then use a motorboat that travels at a speed of 20 mph in still water. John goes by land to a dock and then travels on a river against a current of 4 mph. He reaches his parent's home in 4.5 hours. The return trip takes him 3.5 hours. How far do his parents live from his house?
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speed of 60 mph on land let distance be x
and then use a motorboat that travels at a speed of 20 mph in still water.
against current speed = 20-4=16 mph. River distance be y
Time forward journey
x/60 +y/16 = 4.5
Time return motorboat
speed = 20+4 =24 (with current)
x/60+y/24 =3.5
x/60 +y/16 = 4.5
60y+16x= 60*16*4.5
x/60+y/24 =3.5
60y+24x = 60*24*3.5
16.00 x + 60.00 y = 4320.00
24.00 x + 60.00 y = 5040.00 .............2
Eliminate y
multiply (1)by -1.00
Multiply (2) by 1.00
-16.00 x -60.00 y = -4320.00
24.00 x 60.00 y = 5040.00
Add the two equations
8.00 x = 720.00
/ 8.00
x = 90.00
plug value of x in (1)
16.00 x + 60.00 y = 4320.00
1440.00 + 60.00 y = 4320.00
60.00 y = 2880.00
y = 48.00
Ans x = 90.00
y = 48.00
The time spent on land is the same for both legs or the trip. The 1 hour difference between the times for the two legs is the difference in the time going upstream against the current and the time returning downstream with the current.
The upstream speed is 20-4=16mph; the downstream speed is 20+4-24mph. Determine the distance on the river if the upstream trip takes 1 hour more than the downstream trip.
The distance on the river is 48 miles.
Determine the amounts of time for the upstream and downstream trips.
