Question 245710: can you please help me with this word problem:
two motorist set out at the same time to go from A to B, a distance of 100 miles. they both followed the same route and traveled at different, though uniform, speeds of an integral number of miles per hour. the difference in their speeds was a prime number of miles per hour, and after they had been driving for two hours, the distance of the slower car from A was five times that of the faster car from B. how fast did the two motorist drive?
thank you.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! two motorist set out at the same time to go from A to B, a distance of 100 miles.
they both followed the same route and traveled at different, though uniform, speeds of an integral number of miles per hour.
the difference in their speeds was a prime number of miles per hour, and after they had been driving for two hours, the distance of the slower car from A was five times that of the faster car from B.
how fast did the two motorist drive?
:
Let x = speed of 1
Let p = difference between the speeds of the two cars
then
(x - p) = speed of car 2
:
" after they had been driving for two hours, the distance of the slower car from A was five times that of the faster car from B
:
After two hrs
2(x-p) = car 2 dist from A
100 - 2x = car 1 dist from B
:
the equation
5(2(x-p)) = 100 - 2x
10x - 10p = 100 - 2x
-10p = 100 - 2x - 10x
10p = 12x - 100; multiplied by -1
p =  x - 10
p = 1.2x - 10
the only prime number that will be generated by this equation is 2, (x=10)
therefore
Car 1 speed is 10 mph
Car 2 speed is 8 mph
;
:
We can check this
Car 1: 100 - 2(10) 80 mi from B
Car 2: 2(8) = 16 mi from A
:
80 mi = 5(16) mi
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