Question 1199506
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b = speed of the boat in still water
c = speed of the current
Speeds are in mph


Downstream:
The boat speeds up to go from b to b+c
It travels the 32 mile distance in 1 hour
distance = rate*time
32 = (b+c)*1
32 = b+c
b = 32-c


Upstream:
The boat is slowed down go from b to b-c
This time it takes 4 hours.
distance = rate*time
32 = (b-c)*4
32 = (32-c-c)*4 ..... plug in b = 32-c
32 = (32-2c)*4
32 = 128-8c
32+8c = 128
8c = 128-32
8c = 96
c = 96/8
c = 12
The speed of the current is 12 mph.


Then lastly,
b = 32-c
b = 32-12
b = 20
The boat's speed in still water is 20 mph.


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Check:


b = 20 = speed of the boat in still water
c = 12 = speed of the current


b+c = 20+12 = 32 mph is the boat's speed when going downstream, when the boat is given a helpful push by the water.


Then note how
distance = rate*time
32 = 32*1
32 = 32
Confirming the downstream equation is correct.


b-c = 20-12 = 8 mph is the upstream speed.
distance = rate*time
32 = 8*4
32 = 32
The upstream equation is confirmed also.


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Answers:


Speed of the boat in still water = <font color=red>20 mph</font>
Speed of the current = <font color=red>12 mph</font>
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