Posted by **anthony** on Friday, March 20, 2009 at 6:44pm.

Solve the problem. A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.

- math -
**bobpursley**, Friday, March 20, 2009 at 7:39pm
Downstream: 48=(vb+vs)3

upstsream: 46=(vb-vs)6

multiply the first equation by 2

1) 96=6vb+6vs

2) 46=6vb-6vs

subtract the equations:

50=12vs solve for vs.

- math still need help -
**anthony**, Friday, March 20, 2009 at 8:19pm
i don't understand the way this is being worded. where did 46 come from? what does vs and vb stand for?

- math -
**GanonTEK**, Friday, March 20, 2009 at 8:57pm
There is a mistake in bobpursley's equations - both should have the same distance of 48.

vs = velocity of stream

vb = velocity of boat

and Distance = Velocity*Time

Downstream

48 = (vb + vs)*3

The stream velocity is +ve as the time is shorter downstream - the stream helps

So vb + vs = 16

Upstream

48 = (vb - vs)*6

The stream velocity is -ve as the time is longer so the stream hinders the boat

So vb - vs = 8

Then just solve the 2 equations simultaneously to get vs = 4

Check that and also find the velocity of the boat.

I hope that helps.

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