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

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) (Show Source): You can put this solution on YOUR website!
26.Solve.
15t^2 + 7t = 2
--------------
15t^2 + 7t - 2 = 0
(3t + 2)*(5t - 1) = 0
t = -2/3, 1/5
------------------
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1300 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.34258545910665, -2.67591879243998. Here's your graph:

--------------
Ignore the negative solution
speed =~ 9.34 km/hr
Answer by solver91311(24713) (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

RELATED QUESTIONS
I actually have 2 questions and i am really having problems. i have tried the first one... (answered by jim_thompson5910)
( word prob.) Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of... (answered by jim_thompson5910)
A boat travels 2 km upstream and 2 km back. The time for the round trip is 10 hours. The... (answered by mananth)
A boat travels 1 km upstream and 1km back. The time for the round trip is 10 hours.... (answered by scott8148)
Solve Problems Using Linear Systems 7. Tyler rows 10 km downstream in 2 h. On the return (answered by stanbon)
A boat travels 10 km upstream and 10 km back. The time for the round trip is 10 hours.... (answered by mananth)
Abby rows 10km upstream and 10km back in a total time of 3hrs. The speed of the river is (answered by mananth)
A boat travels 2 km upstream and 2 km back. The time for the round trip is 4 hrs. The... (answered by Shin123,ikleyn)
A boat travels 8 km upstream and 8 km back. The time for the round trip is 2 hrs. The... (answered by mananth)