How do you set up 'upstream/downstream' type problems?

[marissa09]

1. With a tail wind, a plane traveled 800 miles in 6 hours. With a head wind, the plane traveled the same distance in 8 hours. Find the plane's air speed and the speed of the wind.

2. A boat's crew rowed 16 km downstream in 2 hours, but the return trip upstream took 4 hours. What was the rate of the current and the boat's rate in still water?

3. Two miles upstream from his starting point, a canoeist passed a log floating in the river's current. After paddling upstream for one more hour, he paddled back and reached his starting point just as the log arrived. Find the speed of the current.

Help is appreciated.

 

[stapel]

1. With a tail wind, a plane traveled 800 miles in 6 hours. With a head wind, the plane traveled the same distance in 8 hours. Find the plane's air speed and the speed of the wind.

Use the "distance equals rate times time" equation you've always used for this sort of thing, after defining appropriate variables: :wink:

You've been given distances and times; you need two rates. So pick variables for the unknowns that you need to find. Then keep in mind that the plane's speedometer reading only reflects what the engines are doing; the wind will either push the plane forward and speed it up (if it's a tailwind) or else push against the plane and slow it down (if it's a headwind).

Add or subtract the wind's speed from the plane's speedometer reading, accordingly, when you set up your "d = rt" equations. :idea:

If you get stuck, please first read this lessons and, if you still need help, reply showing your work and reasoning. Thank you!

Eliz.

P.S. The other two exercises work exactly the same way.