Question

two ferries simultaneously depart from opposite banks of a river and cross perpendicular to the banks. their speeds are constant, but not equal. the ferries meet 220 yards from the riverbank, and continue along their routes. on their return trips, the ferries meet 100 yards from the other bank. what is the width of the river?

Answer 1

The width of the river is 1700m

What is the time, distance & speed relation?

Speed is calculated by dividing the distance traveled by the amount of time it took to get there. Divide the distance by the speed to find the passing time. To get the distance, multiply the speed by time.

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 when they first meet.....width of the river =   700+ 1000 = 1700 m

Hence, the width of the river is 1700m

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