John and Mike have been friends since school but havent seen

John and Mike have been friends since school but havent seen eachother in many years, so they agree to meet on saturday. John leaves his house at 10:00 am and drives east at 50 miles per hour. Mike leaves his house at the same time and drives west at 45 miles per hour. if their houses are connected by a straight highway running east-west (no stoplight or towns in the way) and are 350 miles apart. How far from johns house will they meet?. at what time will they meet?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let t=time that elapses before they meet
Distance John travels=d
Distance Mike travels=(360-d)
John\'s time=d/50
Mikes\'s time=(360-d)/45
Now we know that John\'s time has to equal Mike\'s time, so:
d/50=(360-d)/45 multiply each side by 50*45 (or cross multiply)

45d=50(360-d) or
45d=18000-50d add 50 d to both sides
45d+50d=18000
95d=18000 divide both sides by 95
d=~189.5 mi------------------------------distance John travels (also distance from John\'s house)
360-d=360-189.5=~170.5 mi---------------------distance Mike travels
John\'s time: t=d/r=189.5/50=3.79 hr-------------3h 47.4m
Mike\'s time: t=d/r=170.5/45=3.79 hr--------------3h 47.4m
Time when they meet=10:00AM + 3h 47.4m=1:47.4pm.
Hope this helps