One last river problem that has me confused

[nyclio]

Maybe it's because of the awkward of this one that I'm not sure why it is what it is. I am looking at physics questions and answers but no work is shown.

If someone could tell me how to set it up, I'd appreciate it:

QUESTION:
A river 1.00 mile wide flows with constant speed of 1.00 mi/hr. A man rows a boat 2.00 mi./hr. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is:

ANSWER:
1.15 hr.

The way I see it, his speed is 3 miles an hour when he is going downstream (rowing speed plus river speed). However, on the return trip, since the current is moving against him at 1 mile an hour (i'm assuming this part), the speed should be reduced to 1 mile an hour. To go downstream at 3 miles an hour, it would take 20 minutes. To return to the starting point, his speed should be 1 mile an hour (since its upstream), and it should take him a full hour, for a total travel time of 80 minutes. However, 80 minutes is 1.33 hrs. Am I on the wrong track?

Thanks again.

 

[what]

Here's a hint he's crossing the river not going upstream and downstream.

 

[xman]

take the components of the velocity, you know the distance traveled in the (x,y) directions if you set your origin at the point where he launches his boat from. find the angle required for him to meet the condition where he lands at exactly the opposite side of the river bank. this problem is basically, relating component parts.

 

[nyclio]

But there are no angles given...and even it's 90 degrees, cos90 = 0 (no horizontal comp.) and vert. comp (1*sin 90) = 1. I am still confused?

 

[libin]

No. You got the idea wrong. When the man is crossing the river, he has to row at an angle with the side to reach the direct opposite point to him because of a current that pushes him sideways. You can definitely calculate the angle here. Once you know that, continue with your problem.

 

[libin]

Draw a diagram and label it properly. It will help you a great deal. This question just need some thinking. First, figure out how long does it actually take for the man to reach the opposite bank IF he is rowing straight (without any angle). Now on your figure should have a triangle. One of the segment is the width of the river, the other the route of the man traveled if he rowed straight. You know both them through given and calcualtions. Then, draw another segment congruent to the route the man rowed but in the opposite direction. Why? Because for him to reach the opposite bank, he had to row at a certain angle. The path that he took must be the same as the other one we just calculated BUT opposing the direction of the current. From there, calculate the time and add them up.