I'm stumped on three things. 1) is the certain speed r or r+4? and 2) do you convert fraction to mixed or decimal form; and 3) do you solve using quadratic equation?

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Answer 1 · 2018-01-23T19:20:32

See below.

Time = distance/speed.

Let #s=speed#

The trip to Burlington is 30 miles. The return trip will obviously be the same distance.

We know the speed on the return journey was 4 mph slower, and the total time for the round trip was #2 3/4# hours.

Writing the two different speeds as:

#s# and #s-4#

So we have:

#30/s+30/(s-4)=11/4#

#(30(s-4)+30s)/(s(s-4))=11/4#

#(120(s-4)+120s)=11s(s-4)#

#11s^2-284+480=0#

Factor:

#(11s-20)(s-24)=0#

#s=20/11# and #s=24#

speed = #11/2=5.5# mph ( not realistic )

So average speed for first part of journey:

#color(blue)(24)# mph.

For second part, speed was 4 mph less, so:

#24-4=20#

Average speed #color(blue)(20)# mph