SOLUTION: Alan and Dave leave from the same point driving in opposite directions, Alan driving at 55 miles per hour and Dave 65 mph. Alan has a one hour head start. How long will they be abl

Question 147112: Alan and Dave leave from the same point driving in opposite directions, Alan driving at 55 miles per hour and Dave 65 mph. Alan has a one hour head start. How long will they be able to talk on their car phones if the phones have a 250-mile range?
Found 2 solutions by giveback, josmiceli:
Answer by giveback(3) (Show Source): You can put this solution on YOUR website!
Let t (in hour) is the time Alan and Dave can talk on their car phone.
Because they are driving from the same starting point but in opposite directons then after t hour, Alan's distance from the start is 55t.
Meanwhile Dave only starts driving 1 hour after Alan, therefore after t hour, Dave's distance from the start is 65(t-1).
The combined distance should be equal or smaller than 250 miles.
From that, we have: 55t+65(t-1)=250 or 55t+65t-65=250 or 120t=315
Then t=315/120 or t=2 hours and (75/120)hour which is 2 hours and 37.5 minutes.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Restated, the problem is, when will the sum of their
distances from the starting point exceed 250 mi?
Assume I have a stopwatch. I will start the stopwatch
when Alan has already driven foor 1 hr.
By then, Alan has driven
mi
I want to find
But now, , Allan's distance from the starting
point is where is the time
showing on my stopwatch.
Now I can write

hr
hr
This is the time after Alan's 1 hr headstart, so they can
talk on their cellphones for
hr
t = 1 hr 37.895 min
t = 1 hr 37 min 54 sec answer
That's it, unless I goofed.
check:

pretty close
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