Two piers, A and B, are located on a river; B is 1500 m downstream from A (Fig. E3.32). 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. How much time does it take each person to make the round trip?

Question

Two piers, A and B, are located on a river; B is 1500 m downstream from A (Fig. E3.32). 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. How much time does it take each person to make the round trip?

Illustration of Diego walking 1800 m and Paul rowing in a river with current.

Diagram showing piers A and B, with a boat and river current for relative velocity problem.

Accepted Answer

Hi, everyone. Let's get started. So two residences, ion residences located upstream and Omega residences located downstream are located along the river sign as showed The distance between the two residences is 1800 m. Diego and Paul must make round trips between the two residences starting from ion residences. Paul is paddling a canoe at a constant speed of 4.50 km/h hour relative to the water in the river. On the other hand, Diego walks on the riverside at a constant speed of 3.7 km/h. The velocity of the stream in the river is 2.60 km/h in the direction from ion to Omega. So it's the river is traveling from left to right. As you can see here, how long will it take for Paul and Diego to make the round trip? So what do we know? We are given a distance De of 1800 m And since we're making a round trip, we're gonna multiply that by two. So our total distance that our friends need to travel is 600 m. Now we're given their speeds in kilometers per hour. So we're going to have to do some converting. Mhm. So Paul's speed on on the river is going to be 4.50 km/h. And Diego's speed walking alongside the river is going to be 3.7 km/h. So first thing I wanna do is convert our distance into kilometers and we're going to use a conversion factor to do that. So one kilometer is equivalent to 1000 m. So are 3600 m should be 3.6 kilometers now because we know that our speed is our distance over time, we can speed equals distance over time. Of course. So we can substitute our values here. I'm gonna start with our friend Diego since he's just walking along the side of the river that makes it a little easier. Yeah. So Diego is moving at 3.7 km/h And he wants to walk 3.6 km. That's gonna be our distance. And our time is what we don't know. That's what we're trying to find. So if we rearrange this equation and solve it, we can conclude that time is approximately 58.4 minutes. That's how long it's going to take Diego to walk to and from the, the residences. So let's see if we can check our answer choices here and cross out any that don't agree with ours. So we can see that our time for Diego and each answer is different in each one. And actually a is the only one that lines up with our value. So answer a time for Diego to travel equals 58.4 minutes And time for Paul to travel equals 72.1 minutes. Must be the correct answer. Thank you.

Verified Solution