Question 987684
A car traveled from city X to city Y at a uniform speed of 120 miles/ hr.
 The car then travels from city Y to city Z at a uniform speed of of 100miles/ hr.
 If the distance the car travelled city X and Y is twice the distance the car travelled between city Y and Z , what is the average speed in miles per hour the car travelled between city X and Z 
:
let a = the average speed of the whole trip
let d = the distance from y to z
 we know the dist from x to y, is twice the dist from y to z, therefore
2d = the distance from x to y
and
3d = the total distance from x to z
:
Write a time equation, time = dist/speed
xy time + yz time = total time
{{{(2d)/120}}} + {{{d/100}}} = {{{(3d)/a}}}
multiply by 600a
600a*{{{(2d)/120}}} + 600a*{{{d/100}}} = 600a*{{{(3d)/a}}}
Cancel the denominators
5a(2d) + 6ad = 600(3d)
10ad + 6ad = 1800d
16ad = 1800d
simplify divide both sides by d
16a = 1800
a = 1800/16
a = 112.5 mph av speed for x to z
:
:
We can confirm this by choosing a value for d, say 100 mi, and finding the times
{{{200/120}}} + {{{100/100}}} = {{{300/112.5}}}
1.67 + 1 = 2.67
:
Equation will be correct for any value of d