Applying variables: river current 3kph, man going 10 km upstream,...

[June]

Hey there, hope your day is going well. I'm back with another question but this time its regarding rationals. Please refer to the following picture.

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5. A man goes fishing in a river and wants to know how long it will take him to get 10 km upstream to his favourite fishing location. The speed of the current is 3 kph, and it takes his boat twice as long to go 3 km upstream as it does to go 4 km downstream. How long will it take his boat to get to his fishing spot?

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	distance	speed	time
downstream	4 km	s + 3	4/(s + 3)
upstream	3 km	s - 3	4/(s + 3)

******* The time for Upstream is suppose to be (4)/(s-3), NOT s+3 - that was my error before taking the photo************

In regards to this question, where would the "twice as long" be applied? I've narrowed it down to two options: Either the upstream speed as ((s-3)/(2)) or would I make the total upstream time 2((4)/(s-3))?

Moreover, would I make both time rationals equal to one another to solve for s and then input it for time for 10k m upstream? Thank you for any help and tips.

June

 

[mmm4444bot]

**** The time for Upstream is suppose to be (4)/(s-3), NOT s+3 …****

Actually, the upstream time is 3/(s-3) because they provided the upstream information in terms of 3km, instead of the 4km used for downstream.

… where would the "twice as long" be applied?

You know the time going upstream is twice as long as the time going downstream (for the given distances), so upstream time is the bigger number. Therefore, the relationship looks like this:

2 × downstream time = upstream time

Substitute your expression for 'downstream time' and substitute the corrected expression for 'upstream time', and then solve for s. You didn't define your variable s, but you understand that s represents the boat's speed in still water, yes?

… then input for time [to calculate the time to go] 10km upstream?

Substitute for s, yes, but not in a time expression. Substitute s into your expression for the rate going upstream. Use that rate and the distance, to find the time. :cool:

 

[June]

Hey mmm4444bot,

I've had to edit this post twice because my stupid self doesn't have a functioning brain at 3:32AM and just caught my mistake following your instructions! Thanks for all you help, I've figured it out

June

 

[June]

Here's my final answer all thanks to you!