# 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.

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Let x be Emily's speed in mph and let c be the speed of the current in mph. Note that Emily rows with the current and Ashley rows against the current.

We have the relation d=rt where d is the distance, r the rate and t the time.

For Emily's trip the distance is 6mi, the time is 1 hour and the rate is x+c ; 6=(x+c)(1)

For Ashleys trip the distance is 6 mi, the time is 2 hours and the rate is x+1-c (1 mph faster than Emily but rowing against the current); 6=(x+1-c)(2)

6=x+c
6=(x+1-c)(2) Divide both sides by 2
---------------
6=x+c

9=2x+1 ==> x=4 ==> c=2

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

(Check: Emily rows with the current so her effective speed is 4+2=6mph; traveling 6 miles will take 1 hour. Ashleys effective speed is 5-2=3mph so it will take 2 hours to cover 6 miles.)

I assume the second part of the question is asking if both women rowed down and back:

Emily rows at 4mph. So for 6 miles she rows at 6mph and for another 6 miles she rows at 2mph. To cover the 12 miles will take 1hour+3hours=4hours.

Ashley rows at 5mph. So for 6 miles she rows at 7mph and for 6 miles she rows at 3mph. To cover the 12 miles will take `6/7` hour+2hours=`20/7` hours or approximately 2.86 hours.

Ashley would finish first by approximately 1.14 hours,