SOLUTION: 26.Solve. 15t^2 + 7t = 2 Solve:#14 Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still wa

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 26.Solve. 15t^2 + 7t = 2 Solve:#14 Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still wa      Log On


   

Question 509175: 26.Solve.
15t^2 + 7t = 2


Solve:#14
Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.


My math friends please help me with these I am on a deadline, thank you.I really am desperate here.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
26.Solve.
15t^2 + 7t = 2
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15t^2 + 7t - 2 = 0
(3t + 2)*(5t - 1) = 0
t = -2/3, 1/5
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Solve:#14
Rowing. Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water.
10/(b-5) + 10/(b+5) = 3
10(b+5) + 10(b-5) = 3*(b-5)*(b+5) = 3b^2 - 75
20b = 3b^2 - 75
3b^2 - 20b - 75 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-20x%2B-75+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A3%2A-75=1300.

Discriminant d=1300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+1300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+1300+%29%29%2F2%5C3+=+9.34258545910665
x%5B2%5D+=+%28-%28-20%29-sqrt%28+1300+%29%29%2F2%5C3+=+-2.67591879243998

Quadratic expression 3x%5E2%2B-20x%2B-75 can be factored:
3x%5E2%2B-20x%2B-75+=+%28x-9.34258545910665%29%2A%28x--2.67591879243998%29
Again, the answer is: 9.34258545910665, -2.67591879243998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-20%2Ax%2B-75+%29

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Ignore the negative solution
speed =~ 9.34 km/hr

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


26. Add -2 to both sides. Then factor. 3 times 5 is 15, 2 times -1 is -2, 3 times -1 plus 5 times 2 is -3 plus 10 equals 7.

14. Use distance = rate times time which can also be expressed as time equals distance divided by rate. If you let represent the speed in still water, then the upstream rate is because the current works against you going upstream and the downstream rate is . Then let represent the time it took to go upstream. Since the total trip took 3 hours, the time to go downstream must be .

First describe the upstream trip using time equals distance divided by rate:



Then describe the downstream trip the same way:



A little Algebra music, Sammy (while we isolate in that second equation):







Now we have two expressions that equate to something, so set the two right-hand sides equal:



A little more Algebra music while we cross-multiply the proportion and collect like terms:







This ugly thing will defy all of your efforts to factor it, so it is time for the -- Look! Up in the sky! It's a bird! It's a plane! It's - it's SuperQuadratic Formula! -- the Quadratic Formula.









A little calculator work will show you that



and since it is unlikely that Abby got anywhere rowing backwards, we can safely discard this root leaving us with:



As the exact answer. Use your calculator to obtain a numerical approximation to the precision you require.

John

My calculator said it, I believe it, that settles it
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