Problem Solving

BTGmoderatorDC wrote:If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3600000x

We want to convert meters per second to kilometers per hour

First, since 1 kilometer = 1000 meters, we can also say that 1 kilometer/1000 meters = 1
Second, since 3600 seconds = 1 hour, we can also say that 3600 seconds/1 hour = 1

This means that multiplying a value by 1 kilometer/1000 meters is the SAME AS multiplying that same value by 1.
Likewise, multiplying a value by 3600 seconds/1 hour is the SAME AS multiplying that same value by 1.

So, x meters/second = x (meters/second)(1)(1)
= x (meters/second)(1 kilometer/1000 meters)(3600 seconds/1 hour)
= x (3600/1000)(kilometers/hour) [after all of the "unwanted" units cancel out]
= x (18/5)(kilometers/hour)
= 18x/5 kilometers/hour
= C

Cheers,
Brent

BTGmoderatorDC wrote:If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3600000x

There are 3,600 seconds in an hour and 1,000 meters in a kilometer. So, let's convert y kilometers/hour to meters/second:

We can start by converting y kilometers to meters.

y kilometers = 1,000y meters

Next we can convert 1 hour to seconds.

1 hour = 3,600 seconds

Thus, y km/hr can be expressed as 1,000y/3,600 m/sec, or 5y/18 m/sec, after it's simplified.

Since our two rates are equal, x = 5y/18. We need to solve this equation for y.

18x = 5y

18x/5 = y

Answer: C