Exercise 43 Page 688

We are told that a jet's groundspeed from Los Angeles (LA) to New York City (NYC) is 100 mi/h faster than the groundspeed from NYC to LA. If we let r be the jet's groundspeed from NYC to LA, we can write expressions to represent the jet's groundspeed for each situation. From NYC to LA:& r From LA to NYC:& r+100 We want to find the round-trip air time.To do so let's recall that the amount of time t spent traveling is the ratio of the distance d traveled to the corresponding speed r. Time=Distance/Speed ⇔ t=d/r

We know that the distance between the cities is 2500 miles. Now, having also the corresponding rates in terms of r, we can write the air-time expressions in terms of the distance and the speed for each case.

	Distance (mi)	Groundspeed (mi/h)	Time (h)
From NYC to LA	2500	r	t_1=2500/r
From LA to NYC	2500	r+100	t_2=2500/r+100

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

t=t_1+t_2

SubstituteII

t_1= 2500/r, t_2= 2500/r+100

t= 2500/r+2500/r+100

Notice that there are no common factors between the denominators. Therefore, the least common denominator is r(r+100). Let's use it!

t=2500/r+2500/r+100

ExpandFrac

a/b=a * ( r+100)/b * ( r+100)

t=2500( r+100)/r( r+100)+2500/r+100

ExpandFrac

a/b=a * r/b * r

t=2500(r+100)/r(r+100)+2500 r/(r+100) r

CommutativePropMult

Commutative Property of Multiplication

t=2500(r+100)/r(r+100)+2500r/r(r+100)

Since we now have like denominators, we can add the numerators.

t=2500(r+100)/r(r+100)+2500r/r(r+100)

Distr

Distribute 2500

t=2500r+250 000/r(r+100)+2500r/r(r+100)

AddFrac

Add fractions

t=5000r+250 000/r(r+100)

Finally, we wrote an expression to describe the total round-trip air time. t=5000r+250 000/r(r+100)