SOLUTION: Please help me: A boat travels for 7 hours. If it tavels 4 hours downstream and 3 hours upstream then it covers the distance of 116 km. But if it travels 3 hours downstream and 4 h

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Question 753825: Please help me: A boat travels for 7 hours. If it tavels 4 hours downstream and 3 hours upstream then it covers the distance of 116 km. But if it travels 3 hours downstream and 4 hours upstream, it covers the distance of 108 km. Find the speed of a boat?

Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
A boat travels for 7 hours. If it tavels 4 hours downstream and 3 hours upstream then it covers the distance of 116 km. But if it travels 3 hours downstream and 4 hours upstream, it covers the distance of 108 km. Find the speed of a boat?
***
let x=speed of boat in still water
let c=speed of current
x+c=speed of boat downstream
x-c=speed of boat upstream
distance=travel time*speed
..
4(x+c)+3(x-c)=116
3(x+c)+4(x-c)=108
..
4x+4c+3x-3c=116
3x+3c+4x-4c=108
..
7x+c=116
7x-c=108
add
14x=224
x=16
speed of a boat=16 km/hr

Answer by josgarithmetic(39623) (Show Source):
You can put this solution on YOUR website!
The assumption that neither of those trips makes necessarily a round-trip.

Let c = stream current speed
let r = the boat speed in no current of steam

Combination___________rate___________time____________distance
4hd,3hu_______________,___4,3__________
3hd,4hu_____________,____3,4___________

The equations making up the system are shown under "distance" column. We are not given any of the rates; only we have times and distances. We can solve the system for both rate variables.

Simplifying the distance equations-----

AND

The simpler system is really