For a portion of the Green River in Utah, the rate of the river's current is 4 mph. A tour guide can row 6 mi down this river and back in 2 h. Find the rowing rate of the guide in calm water. 

I'm having a hard time recalling how o set up a problem like this. I have tried:

with current distance: 6mi

with current rate: x+4

with current time: 6/x+4 

Against current distance: 6mi

against current rate: x-4

against current time: 6/x-4 

Ans:

You have started on the right track. As you have calculated till now, if we

assume that x is the speed of the boat in still water.

Time for downstream = 6/(x+4)

Time for upstream = 6/(x-4)

It is given that the total time (up and down) is 2 hours. So we get the

equation

 Cross multiplying

 Expanding the terms,

 

 Simplifying



This is a standard quadratic equation that you can solve by factorizing.

You get







x = 8 or x = -2

Since x cannot be negative, the speed of the boat in calm water is 8 mph.



Check for correctness:

If speed in still water is 8 mph

Time for downstream = 6/(8+4) = 0.5 hours

Time for upstream = 6/(8-4) = 1.5 hours

Total time = 0.5 + 1.5 = 2 hours.

Correct!



Hope you got it :) 

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
 Make a speed, time, distance table for all of the data and any that you can express from the given data.





Let r = speed of the guide if rowing in still water.

When you say, "6 mi down the river and back", this is 6 miles up the river and 6 miles down the river.  Round trip up and back is 12 miles.  If you believe this is the wrong interpretation then say so.







DIRECTION________speed___________time hours________distance miles

DOWN RIVER_______r+4_____________(___)________________6

UP RIVER_________r-4_____________(___)________________6





The key relation speed*time=distance allows us to make expressions to fill-in times.  

r*h=d for 









DIRECTION________speed___________time hours________distance miles

DOWN RIVER_______r+4_____________(6/(r+4))________________6

UP RIVER_________r-4_____________(6/(r-4))________________6

TOTAL______________________________2_____________________12





He rows up and back in 2 hours.  This allows us to equate to the sum of the time expressions and the only unknown variable is r.



 The problem's principle resulting equation to solve.  The rest of the process is for you to do. 

RELATED QUESTIONS

The speed of a boat in still water is 15 mph. The Jacksons traveled 40 mi down the... (answered by ikleyn,greenestamps)

The rate of a river's current is 2 mph. A rowing crew can row 10mi down the river and... (answered by lwsshak3)

Rowing with the current of a river, a rowing team can row 25 mi in the same amount of... (answered by ankor@dixie-net.com)

Rowing with the current of a river, a rowing team can row 25 mi. in the same amount of... (answered by mananth)

The UP Rowing team can row the 18-kilometer portion of the Agusan river in 3 hours... (answered by addingup,MathTherapy)

Kellen​'s boat travels 20 mph. Find the rate of the river current if she can travel  (answered by jorel1380)

Please show me the solution of this problem: "In 6 hours, two men can row 16 miles... (answered by ankor@dixie-net.com)

 A canoeist can paddle 20.0 mi down a certain river and back in 8.0 h (40.0 mi
round... (answered by richwmiller)

1. Mike can row in still water at a speed twice that of the current in a certain river.... (answered by ankor@dixie-net.com)