SOLUTION: Two ferry boats set out at the same time from opposite banks of a loch. One boat is faster than the other and they pass each other at a point 650 metres from the closer bank. Afte

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Two ferry boats set out at the same time from opposite banks of a loch. One boat is faster than the other and they pass each other at a point 650 metres from the closer bank. Afte      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 898198: Two ferry boats set out at the same time from opposite banks of a loch. One boat is faster than the other and they pass each other at a point 650 metres from the closer bank. After arriving at their destination, each boat remains for 15 minutes to change passengers and then sets out on the return journey. This time, they meet at a point 350 metres from the other bank. How wide was the loch.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two ferry boats set out at the same time from opposite banks of a loch.
One boat is faster than the other and they pass each other at a point 650 metres from the closer bank.
After arriving at their destination, each boat remains for 15 minutes to change passengers and then sets out on the return journey.
This time, they meet at a point 350 metres from the other bank.
How wide was the loch.
:
let w = the width of the loch
:
Draw a diagram for each meeting
A->-----------650-------------->*<-----------(w-650)------------<-B
and
B->--------------------(w-350)----------->*<----------350-------<-A
:
Note on the 1st meeting A travels 650m while B travels (w-650)m
On the 2nd meeting:
B travels 650 + (w-350) which is (w+300)
A travels (w-650) + 350 which is (w-300)
The distance relationship is the same for both trips, we can write a ratio equation
650%2F%28%28w-650%29%29 = %28%28w-300%29%29%2F%28%28w%2B300%29%29
cross multiply
650(w+300) = (w-650)(w-300)
Some tedious FOILing
650w + 195000 = w^2 - 300w - 650w + 195000
650w + 195000 = w^2 - 950w + 195000
Combine like terms on the right
0 = w^2 - 950w - 650w + 195000 - 195000
w^2 - 1600w = 0
w(w - 1600) = 0
then
w = 1600 meters is the width of the loch
:
:
I'll let you check this out, replace w with 1600 in the ratio equation and see if equality reigns!