SOLUTION: A boat travelled 32 miles downstream and then made the return trip. The trip with the current took 1 hour whereas the trip back against the current took 4 hours. What was the speed

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Question 1199506: A boat travelled 32 miles downstream and then made the return trip. The trip with the current took 1 hour whereas the trip back against the current took 4 hours. What was the speed of the boat in still water and what was the speed of the current?

Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

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 = 20 mph
Speed of the current = 12 mph

Answer by greenestamps(13206) (Show Source):
You can put this solution on YOUR website!

The other tutor supplied a good response showing a standard solution method using formal algebra. Since you are presumably studying algebra, you should understand his solution.

But you can get come good mental exercise (and good problem-solving practice) by solving the problem informally using logical reasoning and simple mental arithmetic.

The downstream speed is 32/1 = 32mph; the upstream speed is 32/4 = 8mph.

The downstream speed is the speed of the boat PLUS the speed of the current; the upstream speed is the speed of the boat MINUS the speed of the current. Logical analysis then tells us that the speed of the boat is halfway between 32mph and 8mph, which is 20mph. And that makes the speed of the current 12mph.

ANSWERS: boat speed 20mph, current speed 12mph