## Monday, April 9, 2012

### solution to last week's MGRE Math Beast Challenge

From MGRE, this explanation for why the answer to last week's Math Beast Challenge is indeed (C), 36:

In situations in which two people, animals, cars, etc. are traveling on a straight line:

ADD the rates when moving in opposite directions.
SUBTRACT the rates when moving in the same direction.

In this case, if the prey is running at 40 kph and the predator is chasing at 48 kph, then the predator is catching up at a rate of 8 kph.

Since the distance between the two is 80 meters, we can simply use the formula Rate × Time = Distance.

However, note that the distance is in METERS and the rate is in KILOMETERS per hour. We will have to convert. Let’s use 1 kilometer = 1,000 meters to make a proportion:

80 = 1,000x
0.08 = x

Thus, the distance = 0.08 kilometers.

From Rate × Time = Distance,
8t = 0.08
t = 0.01

Thus, the time is 0.01 or 1/100 HOURS, but we need our answer in SECONDS. 1/100 of an hour is 60/100 of a minute, which is 3/5 of a minute, which is 36 seconds.

Or, make a proportion:

x = (0.01)(3600)
x = 36