John and William leave their home traveling in opposite directions on a straight road. John drives 20 miles per hour faster than William. After 4 hours they ar 250 miles apart.
a. Define a variable for Johns rate.
b. Write an expression for William's rate.
c. Write and solve an equation to find John's rate. Then find William's rate. Make sure to show your work.

Question

anonymous · Answer

a.  call the speed of William, v, then John's speed,w, is 20 mph more than v, or w=v+20

b.  Well, both johnny and billy boy contribute to their distance apart.  The sum of their contributions has to be the total distance apart =250 miles.  We have:
$$vt+wt=250$$Where t is the time (recall speed multiplied by time is the distance travelled).  But we can write w in terms of v as per part a:$$vt+(v+20)t=250$$Oh yeah, they give us the elapsed time here too.  It is t=4 hours.  So, we solve for v:$$4v+4v+80=250$$And,$$v=21.25$$So billy boy's rate is v=21.25 mph.

c. John's is 20mph more than billy's so w=21.25+20=41.25mph

anonymous · Answer

As a check we note that the total distance travelled by Will added to the total distance travelled by John better equal 250 miles.  Does it?

John:  (41.25 miles/hr)(4 hr)=165 miles
William:  (21.25 miles/hr)(4 hr)=85 miles
Adding them up 165+85=250 miles

All good.