Question 553934
Joe drove at the speed of 45 miles per hour for a certain distance.
 He then drove at the speed of 55 miles per hour for the same distance.
 What is the average speed for the whole trip?
:
Let d = distance driven at each speed
then
2d = distance of the whole trip
:
let a = the average speed for the whole trip
:
Write a time equation; time = dist/speed
:
45mph time + 55mph time = total time
{{{d/45}}} + {{{d/55}}} = {{{(2d)/a}}} 
Multiply by the LCM of 45 and 55, 495a
495a*{{{d/45}}} + 495a*{{{d/55}}} = 495a{{{(2d)/a}}}
cancel the denominators;
11ad + 9ad = 495(2d)
20ad = 990d
divide both sides by d
20a = 990
a = 990/20
a = 49.5 mph is the average speed for the trip
:
;
:
Let's check this out, using an assigned distance of 200 mi
{{{100/45}}} + {{{100/55}}} = {{{(200)/49.5}}}
2.22 + 1.82 = 4.04
4.04 = 4.04; confirms our average speed of 49.5 mph