ashiima wrote:
Starting from the same point, a sparrow and a hawk flew in opposite directions. Each traveled at a constant speed until they were 200 feet apart. How far did the sparrow travel?
(1) The ratio of the sparrow's speed to the hawk's speed was 3 to 2.
(2) The average speed of the sparrow was 5 feet per second faster than the average speed of the hawk.
Statement 1:
Let the speed of sparrow be 3.
Let the speed of hawk be 2.
Let the distance covered by sparrow be d.
Hence the distance covered by hawk = 200 - d
Hence the time taken by sparrow = d/3
Hence the time taken by hawk = (200 - d)/2
The times the birds flew in opposite directions is equal.
Hence we can equate the two time equations as follows:
d/3 = (200 - d)/2
This will give you a unique value for d (the distance covered by sparrow. Even if the speeds are assumed to be different (6 & 4), the distance traveled by the sparrow will be the same because the ratio of the speeds is given.
Statement 2:
Let the average speed of hawk be h.
Hence the average speed of sparrow is h + 5.
Using the same logic as above, we can set up an equation for the times taken by each bird.
Time taken by sparrow = Time taken by hawk
i.e. d/(h + 5) = (200 - d)/h
This equation cannot be solved because we have two unknowns and only a single equation.
Hence, the answer is A.