b Substitute the athlete's speed into the expression that you found in Part A.
A
a 9200/3x
B
b About 76 minutes and 40 seconds
Practice makes perfect
a We are told that in a triathlon athletes swim 400 meters, bike 20 kilometers, and run 5 kilometers. An athlete bikes 12 times as fast as she swims, and runs 5 times as fast as she swims. We are given an expression that represents the total time that she needs to complete this triathlon.
400/x + 20 000/12x + 5 000/5xWe want to simplify the above expression. Notice that we have unlike denominators. To make the addition, we will rewrite each rational expression using a least common denominator (LCD).
x:& x
12x: & 3 * 4 * x
5x:& 5 * x
LCD: & 3 * 4 * 5 * x ⇒ 60x
We found that the LCD is 60x. Now we can add the terms up by expanding the corresponding numbers to get the LCD. Let's do it!
b We are given that an athlete swims 40 meters per minute. We want to find the total time that she needs to complete the triathlon. To do so, let's substitute x= 40 into the expression that we found in Part A.
Since one minute is 60 seconds, 23 minute is equal to 40 seconds. Therefore, we can conclude that the athlete needs about 76 minutes and 40 seconds to complete the triathlon.
