race ran with is the unit rate

Question

Japan and China ran a race. The first race Japan won by 5 meters. For the 2 race Japan starts 5 meters behind the starting line. If they ran the second race at the same speed as the first. What are the results of the second race? Hint: unit rate

Answer 1

 

Unit rate means it's 1 unit of time. So when you multiply by 1 unit of time it gives the race distance.

 

example :

Japan

10m/min × 1min= 10m race

then China is

5m/min × 1min = 5m (which is 5m short of winning)

 

writing using variables;

Japan's running rate = x m/min over x distance

China's running rate = (x-5) m/min only making it (x-5) distance

 

race 2:

So now the race is a distance (x+5) for Japan and only distance, x for China. Unit rate's remain the same.

 

The winner will cover their respective distances in a lesser amount of time (remember; time = distance/speed)

 

Japan's time = (x+5)/x

 

China's time = x/(x-5)

 

So let's compare these by making the denominator the same .

 

Japan

(x+5)/x × (x-5)/(x-5) = (x-5)(x+5) / x(x-5) = (x²-25) / x(x-5)

 

China

x/(x-5)× (x)/(x) = (x^{2<) / x(x-5)}

 

Now you can see that Japan always wins the second race

 

(x²-25) < x²