The speed of a stream is 6mph. If a boat travels 42miles downstream in the same time that it takes to travel 21miles upstream, what is the speed of the boat in still water?

Question

4n1m0s1ty · Answer

Define downstream as positive and upstream as negative.

Speed of stream, 6mph; speed of boat is v (what we are trying to find); I'll also define the time it takes to move downstream or upstream, t. 

When the boat moves downstream it is pushed downstream by the current, so its speed is the boat speed + current speed (upstream is opposite).

We know that speed = distance/time, and the boat travels 42 miles downstream:

v + 6 = 42/t

and for upstream:

v - 6 = 21/t

You have a system of eq. so just solve for v.

anonymous · Answer

i'm confused i cant seem to get it

4n1m0s1ty · Answer

Do understand up to what I've written so far?

anonymous · Answer

yes i understand the written part the equation i dont understand

4n1m0s1ty · Answer

Its just a systems of equations, so you can just solve it by substitution:

v + 6 = 42/t and v - 6 = 21/t

rearrange v - 6 = 21/t --> (v - 6)t = 21 --> 

t = 21/(v -6)

plug t into the first equation: v + 6 = 42/t

4n1m0s1ty · Answer

then solve for v