Question

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

Answer 1

we need a variable for the rate in still water
what do you pick?

Answer 2

y ?

Answer 3

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

Answer 4

okay so will it be 1.5x+3y=24?

Answer 5

sorry, i was doing something else, didn't get back to the other one you posted

Answer 6

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 \[\frac{24}{3}=8\]

Answer 7

take the average of those to to get the rate in still water

Answer 8

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

Answer 9

vs land observer

speed is water + boat and water - boat

with or against current

Answer 10

so since we don't have the rate for upstream will it be 3x=1.5*24????

Answer 11

you have both distance and time for each trip,

above shown rate is 16 downstream and 8 upstream

Answer 12

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

Answer 13

Then do I have to plug in the rate of the boat going upstream and downstream to that?

Answer 14

oh , the system of equations thing you mentiond before is this

Answer 15

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,

Answer 16

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