Question 115714: Two boats pass each other going in opposite directions. The first boat travels 2 miles per hour faster than the second boat. What is the average speed of each boat if they are 6 miles apart after 2 hours?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of second boat
Then r+2=rate of first boat
Now we know that after the boats pass, they are separating at the rate of (r+(r+2)) mph (Note: Another way to look at this problem is as follows: In two hours, second boat travels 2r mi and the first boat travels 2(r+2) mi. Now we know that these two distances equals 6 mi so 2r+2(r+2)=6 ---divide both sides by 2 and we get the same equation as below)
So our equation to solve is:
r+r+2=6/2 or------------------------(rate=dist/time)
r+r+2=3 subtract 2 from both sides
r+r+2-2=3-2 collect like terms
2r=1 divide both sides by 2
r=1/2 mph-----------------------speed of second boat
r+2=(1/2)+2=2 1/2 mph-----------------speed of first boat
CK
In two hours, the second boat travels 2*(1/2) or 1 mi
In two hours, the second boat travels 2*(2 1/2) or 5 mi
5+1=6
6=6
Hope this helps---ptaylor
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