SOLUTION: ( word prob.) Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of the river is 5 km/h. find abbys speed in still water. i have no idea how to even start

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: ( word prob.) Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of the river is 5 km/h. find abbys speed in still water. i have no idea how to even start      Log On


   

Question 476940: ( word prob.)
Abby rows 10 km upstream and 10 km back in a total of 3 hr. the speed of the river is 5 km/h. find abbys speed in still water.

i have no idea how to even start this one...can someone please help me. when it comes to word problems i really do not have a clue.
thanks in advance
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = speed in still water.


Now let's form equations for the upstream and downstream journeys

Upstream:

d=rt


10=%28x-5%29t


t=10%2F%28x-5%29


So the time to travel upstream is given by the equation t=10%2F%28x-5%29 where 'x' is the speed of the boat in still water.


-----------

Downstream:

d=rt


10=%28x%2B5%29t


t=10%2F%28x%2B5%29


So the time to travel downstream is given by the equation t=10%2F%28x%2B5%29 where 'x' is the speed of the boat in still water.


Now add the two time expressions and set them equal to 3 (since the total time was 3 hrs)


10%2F%28x-5%29%2B10%2F%28x%2B5%29=3


10%28x%2B5%29%2B10%28x-5%29=3%28x-5%29%28x%2B5%29 ... Note: I'm multiplying EVERY term by the LCD (x-5)(x+5) to clear out the fractions.


10%28x%2B5%29%2B10%28x-5%29=3%28x%5E2-25%29


10x%2B50%2B10x-50=3x%5E2-75


20x=3x%5E2-75


0=3x%5E2-20x-75


Now solve for x:


For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-20%2Ax-75=0 ( notice a=3, b=-20, and c=-75)





x+=+%28--20+%2B-+sqrt%28+%28-20%29%5E2-4%2A3%2A-75+%29%29%2F%282%2A3%29 Plug in a=3, b=-20, and c=-75




x+=+%2820+%2B-+sqrt%28+%28-20%29%5E2-4%2A3%2A-75+%29%29%2F%282%2A3%29 Negate -20 to get 20




x+=+%2820+%2B-+sqrt%28+400-4%2A3%2A-75+%29%29%2F%282%2A3%29 Square -20 to get 400 (note: remember when you square -20, you must square the negative as well. This is because %28-20%29%5E2=-20%2A-20=400.)




x+=+%2820+%2B-+sqrt%28+400%2B900+%29%29%2F%282%2A3%29 Multiply -4%2A-75%2A3 to get 900




x+=+%2820+%2B-+sqrt%28+1300+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%2820+%2B-+10%2Asqrt%2813%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2820+%2B-+10%2Asqrt%2813%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%2820+%2B+10%2Asqrt%2813%29%29%2F6 or x+=+%2820+-+10%2Asqrt%2813%29%29%2F6



Now break up the fraction



x=%2B20%2F6%2B10%2Asqrt%2813%29%2F6 or x=%2B20%2F6-10%2Asqrt%2813%29%2F6



Simplify



x=10%2F3%2B5%2Asqrt%2813%29%2F3 or x=10%2F3-5%2Asqrt%2813%29%2F3



So the solutions are:

x=10%2F3%2B5%2Asqrt%2813%29%2F3 or x=10%2F3-5%2Asqrt%2813%29%2F3





For more help, check out this quadratic formula solver.


Now approximate those answers (by use of a calculator) to get x=9.34259 or x=-2.675. Ignore the negative answer (since a negative speed doesn't make sense)


So the speed of the boat in still water is approximately 9.34259 km/h