Question 635903: 1. Cyrus start jogging from a certain point and runs 5 mph. Jaden jogs from the same point 15 minutes later at a rate of 8 mph. How long will it take that Jaden catch up to Cyrus?
2. A truck driving east at 50 mph passes a certain mile marker. A motorcyclist also driving east passes that mile marker 45 minutes If the one motorcyclist is driving 65 mph,how long will it take for the motorcyclist to pass the truck?
3. Two cars meet at an intersection one heading north; the other, south. If the northbound driver drives at 30 mph and the southbound driver at 40 mph, when will they be 30 miles apart?
Answer by graphmatics(170)   (Show Source):
You can put this solution on YOUR website! The distance Cyrus runs in 15 minutes is (15/60)*5=1.25 miles. Let x be the distance the two will travel after the 15 minutes then
1.25+x/8=x/5
40*1.25+5*x=8*x
50=3*x
x=16.6
So 16.6 is the distance the two will travel before they meet. Jaden will travel this distance in (16.6+1.25)/8=17.91/8=2.24=2 hours 14.4 minutes
The distance the truck traveled is 65*(45/60)=48.75 miles. Let d be the distance after the marker that will have been traveled when the motorcycle meets the truck then
45/60+d/65=d/50
130*.75+2*d=2.6*d
97.5=.6*d
d=162.5
The time the motorcycle takes to travel this distance is 2.5 hours. Adding this to the 45 minutes yields 3 hours 15 minutes
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