SOLUTION: I REALLY really need your help on this problem; the homework that this is on is due tomorrow and I have absolutely NO clue on where to start. 'You are riding in car 1 and your

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Question 691969: I REALLY really need your help on this problem; the homework that this is on is due tomorrow and I have absolutely NO clue on where to start.
'You are riding in car 1 and your best friend is riding car 2. Both cars leave from your house and are heading to a birthday party 100 miles away. Both cars are wired with distance bombs. If the bombs get more than 30 miles apart, they will explode. If the cars continue at the rate the are going (car 1 is 60 miles per hour, car 2 is 40 miles per hour), will you and your friend make it to the party??'
Thank you so much to whomever solves this/ helps me on this!! :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is asking if the cars ever get 30 miles
apart at or before the time that the fastest one
gets to the party 100 miles away
-------------
Let +d+ = the distance between them
Let +t+ = the time in hours from when
they both leave my house.
-------------
+d+=+60t+-+40t+
(1) +d+=+20t+
------------
How long does it take the fastest car to go 100 miles?
+100+=+60t+
+t+=+100%2F60+
+t+=+1.667+
--------------
Plug this into (1)
+d+=+20%2A1.667+
+d+=+33.333+
--------------
This says that when the fastest car gets to the party, there is
already 33.333 mi between the cars ( assuming it was a dry
run without the bombs )
--------------
There is +30+ miles between the cars at
(1) +30+=+20t+
(1) +t+=+1.5+ hrs after they leave my house
So the slower car has gone
+d%5B1%5D+=+40%2A1.5+
+d%5B1%5D+=+60+ miles
The faster car has gone
+d%5B2%5D+=+60%2A1.5+
+d%5B2%5D+=+90+ miles
+d%5B2%5D+-+d%5B1%5D+=+90+-+60+
+d%5B2%5D+-+d%5B1%5D+=+30+ miles
So the cars blow up 1 hr and 30 min after they leave my house
when the faster car has gone 90 miles
Here's a plot of:
(a) distance vs time for slow car
(b) distance vs time for fast car
(c) the distance between them vs time
+graph%28+400%2C+400%2C+-1%2C+3%2C+-10%2C+120%2C+40x%2C+60x%2C+20x+%29+
Go to +1.5+ on the horizontal axis and draw ( in your head )
a vertical line, This is the "detonation" time and distances