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# HELP

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

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

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

BOSEOK  Aug 29, 2017
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(1)

Note that  Distance / Rate  = Time

Let Emily's rate  = r  mph

Let  Ashley's rate  = [r + 1] mph

And let the current rate  = c

So...Emily travels with the current and we have that

6 / [ r + c ] =   1 hour

6 = [r + c]

c = 6 - r

And  Ashley rows against the current .....so

6 / [ r + 1 - c]  = 2 hours

6  = 2 [ r + 1 - c]

6 = 2 [ r + 1 - (6 -r) ]

6  = 2 [ 2r - 5]

6  = 4r - 10

16  = 4r

r   = 4 mph   .....this is Emily's rate

So Ashley's rate  = 5 mph

And the rate of the current  =  6 - r  =  6 - 4  = 2 mph

(2)

For a round trip

Emily would take     6 / [ 4 + 2]  + 6 / [ 4 - 2 ]  =  1 + 3 =  4 hrs

Ashley would take  6 / [ 5 + 2]  + 6 / [5 - 2]  =  6/7 + 6/3  = 6/7 + 2 = 20/7  hrs  ≈ 2.86  hrs

CPhill  Aug 29, 2017

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