SOLUTION: Hi! I am the father of an exasperated 9th grader. Thank you SO MUCH for being there! Here is the question that is stumping her: A boat travels 35km upstream and then back again

Question 1060014: Hi! I am the father of an exasperated 9th grader. Thank you SO MUCH for being there! Here is the question that is stumping her:
A boat travels 35km upstream and then back again in 4 hours 48 minutes. If the speed of the boat in still water is 15km/hr, what is the speed of the current?
Thank you,
Tim in Massachusetts
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
.
Hi! I am the father of an exasperated 9th grader. Thank you SO MUCH for being there! Here is the question that is stumping her:
A boat travels 35 km upstream and then back again in 4 hours 48 minutes. If the speed of the boat in still water is 15 km/hr, what is the speed of the current?
Thank you,
Tim in Massachusetts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "v" be the speed of the current, in km/h.

Then the speed of the boat traveling upstream   is (15-v) km/h,
     the speed of the boat traveling downstream is (15+v) km/h.

The time traveling 35 km upstream   is  hours.
The time traveling 35 km downstream is  hours.

The total time is 4 hours 48 minutes =   hour =   hour =  hour, 
which gives an equation 

 = .

To solve it, multiply both sides by 5*(15-v)*(15+v). You will get

35*5*(15+v) + 35*5*(15-v) = 24*(225-v^2),

24v^2 = 24*225 - 2*35*5*15 = 150,

v^2 =  = ,

v =  =  = 2.5 km/h.

Answer.  The speed of the current is 2.5 km/h.

Solved.

RELATED QUESTIONS
I homeschool my son - 9th grader - we have just started Expressing square roots and there (answered by stanbon)

Hi there! I am not very good at math and I have been stuck on this question for 20... (answered by macston,josmiceli)

Let me start by saying I am 37 and have taken on homeschooling for my 7th and 9th grader. (answered by fcabanski)

Hi I need your help on a question that is stumping me A lottery game requires a... (answered by DrBeeee)

Hi, there is this question that had been stumping me for a while. You can become a... (answered by josmiceli)

Hi there. I have been stuck on this for hours! Here is the following question. The... (answered by Earlsdon,stanbon,jim_thompson5910)

I homeschool my 9th grader and we have one more question on simplifying radicals. He is... (answered by Fombitz)

Hi there. I am having a little difficulty figuring out probability. I think I may know... (answered by sudhanshu_kmr)

Hi there, Hope you're doing well. Here is a question from my unit 1 (derivatives)... (answered by math_helper)