boat speed

Question

don Williams uses his small motorboat to go 3 miles upstream to his favorite spot. Against the current, the trip takes 3/5 hour.With the current it takes 1/5 hour. HOw fast can the boat travel in still water? what is the speed of the current?

Answer 1

Distance = rate x time. The distance is 3 miles, so 3 = rate x time. Letting r represent the speed in still water and c the speed of the current, we have 3 = (r-c) (3/5) = (r-c)(0.6) = 0.6(r-c) for what happens against the current and 3 = (r+c) (1/5) = (r+c)(0.2) = 0.2(r+c) for what happens with the current. 

Against the current:  3 = 0.6(r-c) implies 5 =r-c, or r-c = 5.

With the current:  3 = 0.2(r+c) implies 15 = r+c, or r+c =15.

Adding these two equations together, we have 2r=20, or r=10. By substitution into either equation we have c=5.

Therefore, the boat travels 10 miles per hour in still water with the speed of the current being 5 miles per hour.

Answer 2

 GUIDE PROBLEMS

Let d be the distance traveled by the boat, v0 - speed of the boat in still water, v - speed of the current, t1 = 1/5, and t2 = 3/5.
To find the speed of the boat in still water we have to write two equations: one for motion up the river and another one – against the river.
d/t1 = v0 +v

d/t2 = v0-v

By adding these two equations we will obtain
d(1/t1 + 1/t2) = 2 v0
Substituting the numbers given into the last equation and dividing both sides by 2 we will find v0 = 10mi/hour. If you subtract these equations and repeat the same substitutions, you will obtain: v = 5mi/hour. Thus, your answers are
V0 = 10 mi/h v = 5 mi/h

Answer 3

Let Vb be the speed of the boat and Vc be the speed of the current.

 

Time = distance/speed

 

Upriver the boat and current are moving in opposite directions, so the speed of the current is subtracted from the speed of the boat:

3/5 hour = (3 miles)/(Vb-Vc)                

Vb - Vc = 5 mph

Vb = Vc + 5 mph

 

Downriver the boat and current are moving in the same direction so their speeds add:

1/5 hour = (3 miles)/(Vb+Vc)

Vb + Vc = 15

Substitute Vc+5 in place of Vb:

(Vc + 5) + Vc = 15

2Vc = 10

 

Vc = 5 mph

 

Vb = Vc + 5 = 5+5 = 10 mph