# math

posted by .

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 -

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 -

i don't understand the way this is being worded. where did 46 come from? what does vs and vb stand for?

• math -

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.