SOLUTION: Emily's boat goes 14 mph. Find the speed of the current in the river if she can go 8 miles downstream in the same time as she can go 6 miles upstream.

Question 591708: Emily's boat goes 14 mph. Find the speed of the current in the river if she can go 8 miles downstream in the same time as she can go 6 miles upstream.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let s=speed of the current
Emily's speed upstream=14-s
Her speed downstream=14+s
time required to go 6 miles upstream=6/(14-s)
time required to go 8 miles downstream=8/(14+s)
and we are told that these times are the same, sooooo
6/(14-s)=8/(14+s) multiply each term by (14-s)(14+s) or just cross-multiply and we get:
6(14+s)=8(14-s) or
3(14+s)=4(14-s)
42+3s=56-4s
7s=14
s=2 mph----speed of current
CK
Emily's speed upstream=14-2=12mph
Her speed downstream=14+2=16 mph
time required to go 6 mi upstream=6/12=1/2 hr
time required to go 8 mi downstream=8/16=1/2 hr
Hope this helps ---ptaylor

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