anonymous
  • anonymous
Set as a system of equation then solve: It takes a boat 1.5 hours to go 24 miles downstream and 3 hours to return upstream to its starting point. What is the boat's rate in still water? Please help me
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
we need a variable for the rate in still water what do you pick?
anonymous
  • anonymous
y ?
anonymous
  • anonymous
or better still lets find the rate going against the current, and the rate going with the current that is easier, since you know both

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anonymous
  • anonymous
okay so will it be 1.5x+3y=24?
DanJS
  • DanJS
sorry, i was doing something else, didn't get back to the other one you posted
anonymous
  • anonymous
distance is rate times time, and rate is distance divide by time, so the rate going downstream is \[\frac{24}{1.5}=16\] and the rate going upstream is \[\frac{24}{3}=8\]
anonymous
  • anonymous
take the average of those to to get the rate in still water
DanJS
  • DanJS
d = r * t same distance down and up rate down * time down = rate up * time up when the water is moving also in same direction as boat, the relative rates are different
DanJS
  • DanJS
vs land observer speed is water + boat and water - boat with or against current
anonymous
  • anonymous
so since we don't have the rate for upstream will it be 3x=1.5*24????
DanJS
  • DanJS
you have both distance and time for each trip, above shown rate is 16 downstream and 8 upstream
DanJS
  • DanJS
the velocity of the water and the velocity of the boat , are both relative, with respect to , a land spot, where the distance is 24
anonymous
  • anonymous
Then do I have to plug in the rate of the boat going upstream and downstream to that?
DanJS
  • DanJS
oh , the system of equations thing you mentiond before is this
DanJS
  • DanJS
Given the distance and time down and back, you get the net rate in both directions those rates are a combo of both water and boat speeds,
DanJS
  • DanJS
the overall velocity down is 16 which is both the water and the boat velocities, back the overall rate is 8 and that is the water - boat velocities 16 = W + B 8 = W - B W = 12 B = 4

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