speed: Math?

Question

It takes a boat on a river 2 hours to travel 28 miles downstream and 3 hours to travel 30 miles upstream. What is the speed of the boat and the current of the river.Solve by using systems of equations.

Answer 1

let c be the speed of the current
let b be the speed of the boat

(b+c)2 = 28
(b-c)3 = 30

b+c = 14
b-c = 10

2b = 24
b= 12

12+c = 14
c = 2

speed of the boat is 12 mi/hr
speed of the current is 2mi/hr

Answer 2

This is a rate, time, distance problem. That is, the rate (speed) times the time equals the distance. This is the base of our system of equations.

Lets look at the problem:
"It takes a boat on a river 2 hours to travel 28 miles downstream"
What is the speed of the boat? Well downstream would imply that the boat is traveling with the current. We know that r*t=d. Lets plug in the values.
r*2hours=28miles. Thus, the rate downstream is 14mph.

"3 hours to travel 30 miles upstream."
Lets do the same thing.
r*t=d, r*3=30. Thus the rate upstream is 10mph.

So those are the speeds of the boats, 14 downstream and 10 upstream. But what is the speed of the current? Well we know that the speed of the current always has to be the same. So we think about it this way.

Downstream is speed of boat+speed of current.
Upstream is speed of boat-speed of current.

Using 14 and 10, we find that the speed of the current is 2. And the original speed of the boat is 12 in still water.

Hope this helps!

Answer 3

let x be the speed of the boat and y be the current of the river

2x+2y = 28 (downstream, current is actiing with boat)
3x-3y = 30 (upstream, current is acting again boat)

multiply top by 3 and bottom by 2, add and eliminate

6x+6y = 84
6x-6y = 60
12x = 144
x = 12 mph

substitute into one of the original equations

2x+2y=28
24+2y = 28
2y=4
y =2

boatspeed: 12 mph
current speed 2mph (had you'd ask for a velocity this would be negative to indicate the direction is opposite the boat's)

Answer 4

speed = distance/time
v = d/t
first: v= 28/2
v= 14 miles/hr upstream

second v=30/3
v=10 miles/hr. downstream

now v1-v2= current of river.
= 4 miles/hr
speed of the boat i think u take both speeds v1 and v2.