boat goes 240 miles down stream in the same time it can go 160 miles upstream. speed of the current is 5 miles per hour. speed of the boat in still water?

Question

I would really like a formula to work by but I have yet to find one

Answer 1

PROBLEM

 

boat goes 240 miles down stream in the same time it can go 160 miles upstream. speed of the current is 5 miles per hour. speed of the boat in still water?
I would really like a formula to work by but I have yet to find one

 

SOLUTION

 

Remember DISTANCE = RATE · TIME. So, in this case RATE = Speed of the boat. Also,

 

SPEED_downstream = SPEED_{boat in still water} + SPEED_current

 

SPEED_upstream = SPEED_{boat in still water} - SPEED_current

 

Since DISTANCE = SPEED · TIME, you can rearrange the equation to solve for TIME = DISTANCE / SPEED.

 

Since TIME_upstream = TIME_downstream, you can set

 

DISTANCE_upstream / SPEED_upstream = DISTANCE_downstream / SPEED_downstream and then

 

SOLVE for SPEED_{boat in still water}

 

I hope this helps...

Answer 2

d = rt, so t = d/r, and the times are equal.

 

240/(r + 5) = 160/(r - 5)

 

Cross multiply and solve for r.