# Emily rows six miles downstream in 1 hour and her friend Ashley, rowing 1 mile per hour faster completes the return trip in 2 hours. Find the speed of the current (c) and each girl's rowing...

Emily rows six miles downstream in 1 hour and her friend Ashley, rowing 1 mile per hour faster completes the return trip in 2 hours.

Find the speed of the current (c) and each girl's rowing speed.

If Emily and Ashley were rowing separately, who would complete their trip first and by how long? Round to the nearest hundredth, if necessary.

I think I need to use a rational expression to solve this problem; however, I am not sure how to write it.

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let Emily's speed be r in mph. Then Asley's speed will be (r+1) in mph.

We use distance equals rate times time or d=rt:

For Emiy's trip downstream she rows with the current; if the speed of the current is c then her rate is r+c.
So 6=(r+c)(1) 88 time is 1 hour ==> c=6-r

For Ashley's trip upstream she rows against the current; again with the speed of the current c we have her rate as r+1-c. (1 mph faster rowing than Emily, but against the current so subtract.)
So 6=(r+1-c)(2) **time here is 2 hours ==> c=r-2

Then 6-r=r-2 ==> r=4.

Thus Emily's rowing speed is 4mph, the current's speed is 2mph, and Ashley's rowing speed is 5mph.

(Check: rowing with the current Emily goes 4+2=6mph; so she takes 1 hour to row 6 miles. Ashley rows against the current so she goes 5-2=3mph and will take 2 hours to row 6 miles.)

If Emily rowed down and back at 4 mph she would travel 6 miles at 6 mph and 6 miles at 4-2=2mph. It would take 1 hour for the downstream leg and 3 hours for the upstream leg for a total of 4 hours.

If Ashley rows down and back at 5mph she will travel 6 miles at 5+2=7mph downstream and 6 miles at 5-2=3mph upstream. The downstream leg will take `` of an hour while the upstream leg will take 2 hours for a total of `` hours.

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The current flows at 2mph. Emily's rowing speed is 4mph (without considering current) while Ashley's rowing speed (again without considering current) is 5mph.

Emily's round-trip time is 4 hours.

Ashley's round-trip time is `` hours.

Ashley finishes first by `` hours or 1.14hours.

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