Expert: Chanda Walker - 1/19/2009

Question
If 2 boats leave opposite banks of same river and one travels faster than other and meet 650m from one bank, they each wait ten minutes at destination before return journey, then on second crossing meet 350m from other bank. How wide is the river? I need the formula rather than answer. I feel i should be able to use time speed distance formula using random numbers to work it out? sq78j

Answer
You are on the right track with time,speed,distance formula.  Here is how to set this up.  No random numbers are needed.

v1, v2 are the speeds of each of the boats.

v1*t + v2*t = d, the distance across the river.

v1*t1 = 650
v2*t1 = d-650


v1*t2 = d - 350
v2*t2 = 350

I think this is a very simple problem that is worded to make it complicated.  Since they say that each boat RETURNED, then the meeting place must be at the same location.  That location is 650m from one bank and 350m from the other.  Therefore, the banks are 1000m apart.


However, we can do the math to prove it.  I've set up the equations.  If you divide (v1*t1)/(v1*t2) you'll be left with an equation for t1/t2.  You can do the same with second velocities.  Equate the two results and solve for d.  In the end you can have two solutions.  d = 0 or d = 1000.  Obviously, d = 0 makes no sense so d = 1000.

Let me know if you need to see the steps.