SOLUTION: Please help with this.
There are two cities, A and B, on the opposite sides of a big lake. Two motorboats leave at exactly the same time: one leaves A going directly to B, while t
Algebra ->
Customizable Word Problem Solvers
-> Misc
-> SOLUTION: Please help with this.
There are two cities, A and B, on the opposite sides of a big lake. Two motorboats leave at exactly the same time: one leaves A going directly to B, while t
Log On
Question 290676: Please help with this.
There are two cities, A and B, on the opposite sides of a big lake. Two motorboats leave at exactly the same time: one leaves A going directly to B, while the other leaves B going directly to A. They each travel at constant speed(s).
The boats meet for the first time 500 meters from A. After each boat reaches its destination it immediately turns around and travels directly back to its starting point. Their second meeting takes place 300 meters from B.
How wide is the lake between A and B? What is the ratio between the speeds of the two boats?
You can put this solution on YOUR website! not miscellaneous category but travel and distance. Did you notice the question is about 2 boats traveling and the distance apart?
r*t=d
We will take this in two parts.
It is best to draw a diagram of what happened.
first meeting
boat a went 500 meters
boat b went x-500 meters
second meeting
boat a went x +300 meters
boat b went x +x-300
The key is that for both legs of the trip the times are the same since they start and end together.
a*t=500
b*t=x-500
t=500/a
t=(x-500)/b
500/a=(x-500)/b
a*T=x+300
b*T=x+x-300
T=(x+300)/a
T=(2x-300)/b
Now we have eliminated the times
(x+300)/a=(2x-300)/b
500/a=(x-500)/b
We have three unknowns with two equations so we can't solve for a,b and x
We can get a ratio of a and b
x =1200 meters from A to B
b=7a/5
You can put this solution on YOUR website! There are two cities, A and B, on the opposite sides of a big lake.
Two motorboats leave at exactly the same time: one leaves A going directly to B,
while the other leaves B going directly to A. They each travel at constant speed(s).
The boats meet for the first time 500 meters from A.
After each boat reaches its destination it immediately turns around and travels
directly back to its starting point.
Their second meeting takes place 300 meters from B.
How wide is the lake between A and B?
What is the ratio between the speeds of the two boats?
:
A >--------------------500*---------------< B
Let d = dist from A to B towns
Meet 1st time
A boat travels 500m,
B boat travels (d-500)
:
:
B >--------------------*300---------------< A
Meet the 2nd time
A boat travels (d-500) + 300 = d-200
B boat travels 500 + (d-300) = d+200
:
Ratio of distance traveled by the two boats remain the same, therefore: =
Cross multiply
500(d+200) = (d-500)*(d-200)
500d + 100000 = d^2 - 700d + 100000
0 = d^2 - 700d - 500d + 100000 - 100000
d^2 - 1200d = 0
d(d - 1200) = 0
d = 0
d = 1200 meters from town A to town B
:
Find the ratio of the boats' speed using
Replace d with 1500 = = 5:7, ratio of the speeds
:
:
Check solution by finding the ratio of
Replace d with 1200 = = = 5:7 ratio
