Hi.
I have a little problem with this question. I did the first two (a) and (b), hopefully I did it ok.
I don't know how to do (c)... if anyone can help I'll be thankful.
A nice exercise on Distance = rate*time
Or distance = (average speed)(time)
-------------------------
a) Half the time at 35 mph, and half the time at 55 mph.
Let D = distance from San Antonio to Houston, in miles.
And T = total time of travel from San Antonio to Houston.
distance = rate*time
35(T/2) +55(T/2) = D
Multiply both sides by 2,
35T +55T = 2D
90T = 2D
Since average speed is D/T, then,
Divide both sides by T,
90 = 2D/T
D/T = 90/2 = 45 mph --------------answer.
------------------------------
b) Half the distance at 35 mph, and half the distance at 55 mph.
time = distance/rate
(D/2)/35 +(D/2)/55 = T
D/70 +D/110 = T
Multiply both sides by 70*110,
110D +70D = 70*110*T
180D = 7700T
D/T = 7700/180 = 42.7777...mph, average speed -------answer.
--------------------------
c) The average speed for the whole trip.
total time = distance/(ave. speed)
a) T1 = D/45 hrs
b) T2 = D/42.7777.... hrs
So, average speed for a) and b) is
= 2D/(T1 +T2)
= 2D/(D/45 +D/42.7777...)
= 2[(45)(42.7777..)] / [42.7777... +45]
= 43.86 mph ----------------------------answer.