I need help on this math problem please
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I need help on this math problem please

[From: ] [author: ] [Date: 11-05-04] [Hit: ]
The third row is the easiest one. Just plug in v = 7 and c = 2 into the formula and simplify. No algebra, just arithmetic.......
In a kayak race, the participants must paddle a kayak 900 meters down a river and then return 900 meters up the river to the starting point (a = 900). Susan has correctly deduced that the total time t (in seconds) depends on the speed c (in meters per second) of the water according to the following expression, where v is the speed of the kayak relative to the water (the speed of the kayak in still water).
t=900/v+c + 900/v-c



Time t (sec)-------Speed of kayak relative to the water v (m/sec)--------Current of the river c (m/sec)
360 ? 6
240 ? 2
? 7 2
300 ? 8

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For each line of your table you have values for two of the three variables t, v, and c. You're supposed to plug in the known variables and solve for the unknown. For the first set of data,

360 = 900/(v+6) + 900/(v-6)

First, let's divide both sides by 180 to get smaller coefficients:

2 = 5/(v+6) + 5/(v-6)

Multiply both sides by (v+6)(v-6):

2(v+6)(v-6) = 5(v-6) + 5(v+6)

Expand and simplify:

2(v² - 36) = 5v - 30 + 5v + 30
2v² - 72 = 10v
2v² - 10v - 72 = 0
v² - 5v - 36 = 0
(v - 9)(v + 4) = 0
v = 9 or v = -4

The negative answer makes no physical sense so we discard it. Therefore, you put 9 in the "v" column in the first row.

The second and fourth rows are done in exactly the same way, and I leave those to you.

The third row is the easiest one. Just plug in v = 7 and c = 2 into the formula and simplify. No algebra, just arithmetic.
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