on a certain river

Question

On a certain river, a paddle boat travels 3 miles upstream (against the current) in the same amount of time it travels 5 miles downstream (with the current). If the current of the river is 1 mile per hour, determine the speed of the boat in still water.

Answer 1

Chelsea:

 

Let the speed of the boat in still water be b mph. Then, upstream, it is b - 1 and downstream it is b + 1, since 1 mph is the speed of the current.  We know that the distance d, speed s and time are connected by the formula

 

d = st, so t = d / s.

 

From the given information, we have the time to travel upstream as 3/(b-1) and the time to travel downstream is 5 /(b+1) But we are also given that the the two times are the same.  Hence

 

3/(b-1) = 5/(b+1)

 

Cross-multiply and re-arrange.

 

3(b+1) = 5 (b-1)

 

2b = 8

 

b = 4

 

Back check. The boat's upstream speed is 4 - 1 - 3 mph.  It will take 1 hour to go 3 miles.  The boat's downstream speed is 4 + 1 = 5 miles.  To go five miles it will take 1 hour, exactly the same time. CHECK

 

Dr. G.

Answer 2

S = speed in still water

 

distance = speed x time

 

3 miles = (s - 1) t

 

5 miles = (s + 1)t

 

3/5 = (s-1)/(s+1)

 

3(s+1) = 5(s-1)

3s + 3 = 5s - 5

8 = 2s

s = 4 miles per hour