SOLUTION: A car travels a total distance of 180 km. After traveling a certain distance, the car experienced an engine trouble and traveled half its original speed and arrived at its destinat

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Question 435730: A car travels a total distance of 180 km. After traveling a certain distance, the car experienced an engine trouble and traveled half its original speed and arrived at its destination 1 hour late. Had the engine trouble occurred 30 km farther, the car would have arrived half an hour late. Find the initial average speed of the car before the engine problem. How to solve this?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A car travels a total distance of 180 km.
After traveling a certain distance, the car experienced an engine trouble and
traveled half its original speed and arrived at its destination 1 hour late.
Had the engine trouble occurred 30 km farther, the car would have arrived half an hour late.
Find the initial average speed of the car before the engine problem. How to solve this?
:
Let s = the normal speed of the car
then
.5s = speed after engine trouble
:
Let d = distance traveled at normal speed
then
(180-d) = distance traveled at half speed
:
Normal time required by the trip: 180%2Fs
:
d%2Fs + %28180-d%29%2F%28.5s%29 = 180%2Fs + 1
multiply equation by s, results
d + 2(180-d) = 180 + s
d + 360 - 2d = 180 + s
-d = 180 - 360 + s
-d = -180 + s
d = 180 - s
:
Equation if the breakdown was 30 mi further
%28d%2B30%29%2Fs + %28180-d-30%29%2F%28.5s%29 = 180%2Fs + .5
%28d%2B30%29%2Fs + %28150-d%29%2F%28.5s%29 = 180%2Fs + .5
Multiply equation by s, results
d + 30 + 2(150 - d) = 180 + .5s
d + 30 + 300 - 2d = 180 + .5s
-d + 330 = 180 + .5s
-d = 180 - 330 + .5s
-d = -150 + .5s
:
Add the two equations
d = 180 - s
-d= -150 + .5s
0 = 30 - .5s
.5s = 30
s = 60 mph is the initial speed
:
In hit the wrong button and sent this off prematurely, hopefully you will get this.
I will check this solution and add it to this later.