Question 540713
City A and City B are 135 km away. Two cars drove from A to B. 
The first car left 5 hours earlier. 
The second car arrived City B 30 minutes later than the first one.
 If the ratio of the speed of the first to the speed of the second car is 2:5, find the speed of the first car.
:
Let t = travel time of the 1st car
then
t - 5 + .5 = (t-4.5) is the travel time of the 2nd car (left 5 hrs later, arrived a half hr later
:
speed = dist/time
:
{{{135/t}}} = the speed of the 1st car
and
{{{135/((t-4.5))}}} = the speed of the 2nd car
the ratio of the speeds is 2:5
:
{{{135/t}}}
------------- = {{{2/5}}}
{{{135/((t-4.5))}}}
:
Cross multiply
5{{{135/t}}} = 2{{{135/((t-4.5))}}}
:
{{{675/t}}} = {{{270/((t-4.5))}}}
Cross multiply
675(t-4.5) = 270t
675t - 3037.5 = 270t
675t - 270t = 3037.5
405t = 3037.5
t = {{{3037.5/405}}}
t = 7.5 hrs for the 1st car to make the trip
then
7.5 - 4.5 = 3 hrs for the 2nd car.
:
Find the speed of the 1st car
{{{135/7.5}}} = 18 mph
:
Find the speed of the 2nd car to check our solution
{{{135/3}}} = 45 mph 
:
See if the {{{18/45}}} = {{{2/5}}}; both equal .4