SOLUTION: 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 o

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 o      Log On


   

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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Ft = the speed of the 1st car
and
135%2F%28%28t-4.5%29%29 = the speed of the 2nd car
the ratio of the speeds is 2:5
:
135%2Ft
------------- = 2%2F5
135%2F%28%28t-4.5%29%29
:
Cross multiply
5135%2Ft = 2135%2F%28%28t-4.5%29%29
:
675%2Ft = 270%2F%28%28t-4.5%29%29
Cross multiply
675(t-4.5) = 270t
675t - 3037.5 = 270t
675t - 270t = 3037.5
405t = 3037.5
t = 3037.5%2F405
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%2F7.5 = 18 mph
:
Find the speed of the 2nd car to check our solution
135%2F3 = 45 mph
:
See if the 18%2F45 = 2%2F5; both equal .4