MHB How Long Should Milo and Bernard Paddle Downstream to Meet Vince by 5 P.M.?

[paulmdrdo1]

please I need assistance with this problem

help me get started

Roughing It Milo and Bernard are planning a three-day canoe trip
on the Roaring Fork River. Their friend Vince will drop them off at
the Highway 14 bridge. From there they will paddle upstream for
12 hours on the first day and 9 hours on the second day. They have
been on this river before and know that their average paddling rate
is twice the rate of the current in the river. At what time will they
have to start heading downstream on the third day to meet Vince at
the Highway 14 bridge at 5 P.M.?

 

[MarkFL]

I would begin by defining $c$ as the speed of the current. So, how fast will they move upstream and how fast will they move downstream in terms of $c$? If it takes them 9 + 12 = 21 hours to travel upstream, then how long will it take to travel this same distance downstream?

 

[paulmdrdo1]

2c-c = their rate upstream
2c+c = their rate downstream

are these correct?

 

[MarkFL]

Yes, although you can simplify them...

 

[paulmdrdo1]

c = rate upstream
3c = rate downstream

what's next?

21c = distance traveled

21c=3c(t)

t = 7 hours

how do I determine the time?

 

[MarkFL]

Good, since they travel 3 times as fast downstream as upstream it will take them 1/3 as long to travel the distance.

What time is 7 hours before 5 pm?

 

[paulmdrdo1]

It's 10 pm

 

[MarkFL]

Well, it's actually 10 am. :D