Q.34. Simultaneous equations word problem

Question 34.

Two turtles start at the same instant on opposite sides of a field. One is faster than the other. They cross at a point 720 yards from the left side on their way to the other end, where each spends 11.5 minutes to eat before heading back. They meet again at a point 400 yards from the right side of the field.

How wide is the field?

Answer 34.
Let u = speed of the turtle starting from left
and v = speed of the turtle starting from right
and x = width of the field.

From the given information,
720/u = (x - 720)/v ... ... ( 1 ) and
(x - 720)/u + 11.5 + 400/u = 720/v + 11.5 + (x - 400)/v ... ( 2 )

Solving equations ( 1 ) and ( 2 ),
x = 1760 yds.

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