Question 313345: Please help me solve this
2 boats are 110 km apart they travel towards each others one traveling at 5km/hr slower than other if they in 2hr find the speed of each boat
Found 2 solutions by mananth, Theo:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 2 boats are 110 km apart they travel towards each others one travelling at 5km/hr slower than other if they meet in 2hr find the speed of each boat.
Your problem is incomplete.
I have amended the statement. Check.
..
let one boat travel x km/hr
distance traveled by the boat in 2 hours = 2x
The other boat travels at x-5 km/ hr.
distance traveled by this boat = 2(x-5)
..
The total distance = 110 km
2x+2(x-5)=110
2x+2x-10=110
4x=120
x= 30 km/hr speed of first boat
the other boat travels at 25 km/hr.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 2 boats are 110 km apart.
They travel toards each other.
Boat 1 travels 5 km/hr slower than the other.
They meet in 2 hours.
What is the speed of each boat.
This problem deals with R*T = D which means:
Rate (otherwise known as speed) times Time equals Distance.
If I travel for 1 hour at 50 miles an hour, then I will have traveled 100 miles in 2 hours.
R*T = D becomes 50*2 = 100
In your problem, we let x equal the speed of boat 1.
Since boat 1 is traveling 5 km/hr slower than boat 2, the speed of boat 2 must be equal to X + 5.
Boat 1 travels at x km per hour.
Boat 2 travels at (x+5) km per hour.
The total distance that both boats travel is 120 km.
They will meet at some point in the middle.
The total time that each boat takes is 2 hours since they are both traveling at the same time.
The formula for boat 1 becomes:
x * 2 = y
We use y for the distance since we don't know how far boat 1 has traveled.
The formula for boat 2 becomes:
(x + 5) * 2 = z
We use z for the distance since we don't know how far boat 2 has traveled, only we know that it's not the same distance that boat 1 has traveled.
y is the distance that boat 1 travels.
z is the distance that boat 2 travels.
We know that y + z = 110 km because we know that the total distance traveled by both boats is equal to 110 km.
From the Formula of y + z = 110, we can derive y in terms of z, or z in terms of y.
We'll solve for y in terms of z to get y = 110 - z.
This allows us to eliminate y as a variable in the equation.
Our formulas for boat 1 and boat 2 that were:
x * 2 = y
(x + 5) * 2 = z
become:
x * 2 = 110 - z
(x + 5) * 2 = z
We will solve both formulas for z which will allow us to eliminate z as a variable in the equation.
The second formula is already solved for z.
The first formula is:
x * 2 = 110 - z.
Add z to both sides of this equation and subtract (x * 2) from both sides of this equation to get:
z = 110 - (x * 2)
We now have solved for z in 2 equations.
They are:
z = 110 - x*2
z = (x+5) * 2
Since both expressions on the right side of each equation are equal to z, we can set both expressions equal to each other to get:
110 - x*2 = (x+5) * 2
We have now eliminated z as a variable in the equation.
We now have one equation in one unknown which can be solved.
Add x*2 to both sides of this equation to get:
110 = (x+5)*2 + x*2
Simplify this equation by removing parentheses to get:
110 = 2*x + 2*5 + 2*x
Combine like terms and simplify further to get:
110 = 4*x + 10
Subtract 10 from both sides of this equation to get:
4*x = 100
Divide both sides of the equation by 4 to get:
x = 25
If x = 25, then (x+5) must equal to 30
Boat 1 is traveling at x = 25 km per hour.
Boat 2 is traveling at (x+5) = 30 km per hour.
We test out answer to see if it is correct.
Boat 1 travels 25 km per hour for 2 hours which means boat 1 has traveled 50 km.
Boat 2 travels 30 km per hour for 2 hours which means boat 2 has traveled 60 km.
50 km + 60 km = 110 km which is the total distance traveled by both boats.
If they start 110 km apart, they will meet in exactly 2 hours when boat 1 has traveled 50 km and boat 2 has traveled 60 km.
The answer to your question is:
Boat 1 travels at 25 km per hour.
Boat 2 travels at 30 km per hour.
the key to solving this problem is determining equivalencies and reducing the number of unknowns.
Knowing that y + z = 110 allows you to solve for y in terms of z or z in terms of y which eliminates one of the unknowns. In our case, we eliminated z as an unknown.
Setting both equations equal to z and then setting the equations equal to each other allows you to eliminate another of the unknowns. The unknown we we eliminated was z.
Once you're down to one unknown in one equation, solving becomes just a matter of working through the details.
You also need to know the basics of the type of problem which is:
Rate * Time = Distance
This problem could not be solved without knowing that.
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