How much time does it take the walker to make the round trip?

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The discussion focuses on calculating the round trip times for a walker and a rower between two piers, A and B, with B being 1500 m downstream from A. The walker moves at a constant speed of 4.00 km/h, while the rower rows at the same speed but must account for the river's current of 2.80 km/h. For the walker, the total round trip time is derived from the distance and speed, while for the rower, the downstream and upstream speeds are adjusted by the current. The calculations reveal that the walker’s round trip takes approximately 30 minutes, while the rower's round trip takes about 24.5 minutes. The discussion clarifies the meaning of "relative to the water" in terms of effective speed in a flowing river.
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Two piers, A and B , are located on a river: B is 1500 m downstream from A . Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from A to B .

what does "relative to the water" mean?

1.) How much time does it take the walker to make the round trip?
answer must be in mins

2.) How much time does it take the rower to make the round trip? answer must be in mins

my work:

Given:
x=1500m
v(b) = 4.00 km/h
v(w) = 4.00 km/h
v(r) = 2.80

t1 = (1500)/(4+2.80) = 220.588secs <--- downstream time
t2 = (1500)/(4-2.80) = 1250 secs <--- upstream time

t(t) = 1470.588s <--- total time

how would i solve #1 ?

im thinking that i would need the distance formula

x(t) = x(0) + v(0)t + 1/2at^2
2(1500) = 0 + 2.80t + 0 (x(0) = 0, because at t=0, x=0. and a=0 because of constant speed)

3600= 2.80t... nevermind, it doesn't look right, can someone help?
 
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EaGlE said:
2.) How much time does it take the rower to make the round trip? answer must be in mins

my work:

Given:
x=1500m
v(b) = 4.00 km/h
v(w) = 4.00 km/h
v(r) = 2.80

t1 = (1500)/(4+2.80) = 220.588secs <--- downstream time
t2 = (1500)/(4-2.80) = 1250 secs <--- upstream time

t(t) = 1470.588s <--- total time
Basic idea is OK, but you are mixing up units. It's easier than you think. I'll do the first part, the time from A to B:
t1 = D/V = (1.5 Km)/(6.28 Km/hour) = 0.24 hours
How many minutes is that? You take it from here.

how would i solve #1 ?
Exactly the same way, only now the speed is just 4.0 Km/hour both ways. So, t = D/V ...
 
"relative to the water" means that that is his speed treating the water as it were not flowing. The actual or "true" speed is the water's speed added to his boat's speed when he is going down stream with the current, and subtracted from his boat's speed when he is going upstream against the current.
 
thank you, works perfectly
 
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