In a canoe race, a team paddles downstream 560 meters in 70 seconds. The same team makes the trip back upstream to the starting point in 80 seconds. Write a system of two equations in two variables that models this problem.
2007-03-28 16:44:33 · 3 answers · asked by mike 1 in Science & Mathematics ➔ Mathematics
ok, yeah thanks for the frank answer but I really need more of an explination
2007-03-28 16:54:18 · update #1
Let the current speed be c and the team's rowing speed be r.
Going downstream the total speed is r + c = 560/70 = 8 m/s.
Going upstream the total speed is r - c = 560/80 = 7 m/s.
So the equations are
r + c = 8
r - c = 7
If you solve these you will get r = 7.5, c = 0.5. So the team can paddle at 7.5 m/s in still water, and the current is running at 0.5 m/s.
2007-03-28 16:49:30 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
You can do this. Use the fact that
distance = speed * time
You have two cases. The distance is the same in both cases. You are given the time for each case. The only things you don't know are the speed of the canoe in the stream and the speed of the stream itself. The only tricky part is remembering that the total speed is the sum of the canoe and the stream when they are paddling downstream, so your "downstream equation" looks like this:
distance = (canoe speed + stream speed) * time to paddle downstream
When they're paddling upstream, the total speed is the difference betwen the canoe speed and the stream speed, because the canoe is "slowed down" by the water. So your "upstream equation" looks like this:
distance = (canoe speed - stream speed) * time to paddle upstream
So just plug in the numbers you know, and you'll have two equations with two variables. The two variables represent the speed of the canoe and the speed of the stream.
2007-03-28 23:56:12 · answer #2 · answered by Paul O 2 · 0⤊ 0⤋
yup, first guy is right!
2007-03-28 23:52:16 · answer #3 · answered by Q 3 · 0⤊ 1⤋