Exercise 58 Page 689

We are told that a bicycle club rode a 20-mile round-trip route. This means that they rode 10 miles on the fist half of trip and 10 miles on the way back. Additionally, we are given that their averaged rate is 12 miles per hour for the first half of the trip and 15 miles per hour for the way back. We want to find the total hours for the trip. To do so, let's remember the time formula! Time=Distance/Rate ⇔ t=d/r The amount of time t spent traveling is the ratio of the distance d traveled to the rate r. With the distances and corresponding rates for the two halves of the way, let's find out how long they rode!

	Distance (mi)	Rate (mi/h)	Time (h)
First Half of the Trip	10	12	t_1=10/12
Second Half of the Trip	10	15	t_2=10/15

Now we will add the expressions t_1 and t_2 to find the total amount of round-trip time.

t=t_1+t_2

SubstituteII

t_1= 10/12, t_2= 10/15

10/12+ 10/15

We need to rewrite each fraction using the least common denominator. Notice that the least common multiple of 12 and 15 is 60. Let's get equal denominators to complete the addition of fractions.

10/12+10/15

ExpandFrac

a/b=a * 5/b * 5

50/60+10/15

ExpandFrac

a/b=a * 4/b * 4

50/60+40/60

AddFrac

Add fractions

90/60

ReduceFrac

a/b=.a /30./.b /30.

3/2

CalcQuot

Calculate quotient

1.5

In the context of the problem, we can conclude that the round trip took 1.5 hours.