Question

Don Williams wised his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 5/6 hour. With the current the trip takes 1/2 hour. How fast can the boat travel in still water ? What is the speed of the current in still water the boat speed is __ mph. The speed of the current is ___ mph

Answer 1

let s = speed in still water

let c = rate of the current

then

(s-c) = effective speed up-stream

and

(s+c) = effective speed down-stream

Write a distance equation for each way; dist = time * speed

5/6*(s-c) = 5

1/2 *(s+c) = 5

Now we get rid of the fractions

5(s-c)=30

s + c = 10

5s - 5c = 30

s + c = 10

siplifying:

s - c = 6 (1)

s + c = 10 (2)

adding:

2s = 16, then s = 8

8 mph is the boat speed in still water

According with (2):

8 + c = 10, then c = 2

2 mph is the speed of the current