A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
PLEASE HELP
The current in a nearby river is 5 mph. John wants to be able to travel up the river for a
distance of 30 miles and return to his starting point in a total of 8 hours. How fast must John
be able to row his boat in order to accomplish this? (Assume that the speed that John can
row refers to how fast he can row in still water.)
anonymous
 one year ago
PLEASE HELP The current in a nearby river is 5 mph. John wants to be able to travel up the river for a distance of 30 miles and return to his starting point in a total of 8 hours. How fast must John be able to row his boat in order to accomplish this? (Assume that the speed that John can row refers to how fast he can row in still water.)

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1He travels a total time of 8 hours. If he travels up the river for t time, how much time will he travel down the river?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have no idea!! please explain

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. The total trip is 8 hours. time going up + time going down = 8 hours If you let the time going up be called just t, then you have t + time going down = 8 hours Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now let's see if we can get an expression for the time going down. t + time going down = 8 Subtract t from both sides: time going down = 8  t Now we have: Time going up = t Time going down = 8  t Ok?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I put the info we have in the table below. Now we need the speed going up and the speed going down, and the distances going up and down. dw:1436391156182:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's do the distances first bec they are very easy.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1How far does he row each way?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like how am i supposed to know im so confused on this question

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Have you read the problem? It's written right there. There is no calculation needed.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Does this help? \(\sf John ~wants ~to ~be ~able ~to ~travel ~up ~the ~river ~for ~a ~distance ~of ~\huge \color{red}{30 ~miles}\) \( \sf and ~return ~to ~his ~starting ~point ~in ~a ~total ~of ~8 ~hours. \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Right, Each part of the trip is 30 miles. We can add the distances to our table.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436391741905:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to work on the speed going up and the speed going down. His speed in still water is an unknown. Let's call it s. When he goes up the river, does the 5 mph speed of the river speed him up or slow him down?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Right. That means it takes away from his speed. If the speed in still water is s, then going up the river against the 5mph current, his speed will be s  5 By the same token, going down the river, the 5mph current helps him, so his speed will be s + 5 down the river. Now we add the speeds to our table.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436392136839:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now that we have the info how would i answer the question?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now that we have all the info we need, we can solve the problem. speed = distance/time That means distance = speed * time

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We write an equation for going up the river and an equation for going down the river.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Up the river distance = speed * time 30 = (s  5)t Down the river distance = speed * time 30 = (s + 5)(8  t)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we have a system of equations that we need to solve: 30 = (s  5)t 30 = (s + 5)(8  t)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Solve the first equation for t and substitute in the second one: \(t = \dfrac{30}{s  5} \) \(30 = (s + 5)(8  \dfrac{30}{s  5}) \) Now we have an equation in only s, so we can solve for s.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Multiply both sides by s  5 to get rid of the denominator: \(30(s  5)= (s + 5)(s  5)(8  \dfrac{30}{s  5}) \) \(30s  150 = (s + 5)(8s  40  30)\) \(30s  150 = (s + 5)(8s  70) \) \(30s  150 = 8s^2  70s + 40s  350\) \(30s  150 = 8s^2  30s  350 \) \(8s^2  60s  200 = 0\) \(2s^2  15s  50 = 0\) \((2s + 5)(s  10) = 0\) \(s = \dfrac{5}{2} \) or \(s = 10\) We discard the negative speed, 5/2, and the answer is the speed is 10 mph.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's see if the answer makes sense. The speed in still water is 10 mph The speed going up is 5 mph The speed going down is 15 mph The time going up is 30/5 = 6, 6 hours The time going down is 30/15 = 2, 2 hours 6 hours + 2 hours = 8 hours. Yes, 10 mph is the correct speed he needs to row in still water.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0could you help me with this as well?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.