How wide is the river??....?

Question

Two motorboats on opposite shores of a river start moving towards eachother, but at different speeds. Please neglect all other factors like acceleration , turn-around time, and current. When the two boats pass one another the first time, they are 700 meters from one shoreline. Each continues to the opposite shores, then turns around and begins moving towards one another again. When they pass the second time, they are 300 meters from the other shoreline. (Their speeds, though different, remain constant). How wide is the river???

Answer 1

The speed of boat 1 is v1 and the speed of boat 2 is v2. The width of the river is w.

In the first time interval, boat 1 travels 700 meters from the shore it started.
v1*t1=700
boat 2 travels the width of the river less 700 meters
v2*t1=w-700

In the second time interval, boat 1 travels the width of the river less 700 meters plus the width of the river less 400 meters.
v1*t2=2*w-1100

While boat 2 travels 700 meters plus 400 meters
v2*t2=1100

Therefore
v1*t1+v1*t2=w-200
v2*t1+v2*t2=w+400

v1/v2=(w-200)/(w+400)

also
v1*t2-v1*t1=w-900
v2*t2-v2*t1=1800-w

v1/v2=(w-900)/(1800-w)

using the two ratios

(w-200)/(w+400)=(w-900)/(1800-w)
multiply the denominators from both sides to get
2*w^2-2500*w+200*1800-900*400=0
or
w=1250 meters

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