Question

two ferries start moving toward each other from opposite riverbanks, a and b. when they pass each other for the first time, the distance to riverbank b is 100 meters. each ferry starts its return trip as soon as it reaches its destination. when the ferries meet for the second time, the distance to riverbank A is 50 meters. what is the distance between riverbanks a and b? Help I will give 40 points

Answer 1

Let 'x' be the distance from THE far bank   where 700 is the distance to the NEAR bank

boat one has travelled 700    (rate = 700/unit time)         boat two has travelled   x    rate = x / unit time

boat one then travels   x  + 400  more      and boat two travels   700 + (700+x -400) more    when they meet

The time is the same      rate x time = distance      distance/rate = time     equate the distances divided by the respective rates

(700 + x + 400)/700     =    (  x  +  700     +  (700+x-400) )/x

1100x + x^2 = 1400x + 700000

x^2-300x -700000 = 0                         quadratic formula yields  x = 1000  

One boat travels 700   the other   1000 whe they first meet.....width of river =   700+ 1000 = 1700 m