SOLUTION: Sally left the house at 8;00 am and is running at eight miles per hour. Two hours later, Matt left to catch sally, driving his car at 40 mph. At what time will Matt catch Sally?

Question 976811: Sally left the house at 8;00 am and is running at eight miles per hour. Two hours later, Matt left to catch sally, driving his car at 40 mph. At what time will Matt catch Sally?
Found 2 solutions by richwmiller, FrankM:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Gaining speed 40-8= 32 mph
Head start 8*2 =16 miles
Time to catch up 16/32=0.5 hours
Time to catch up =30 minutes
Algebraic solution
8(t+2)=40t
8t+16=40t
16=40t-8t
16=32t
t=0.5 hours or 30 minutes
so they meet at 10:30

Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
Simplest way -
At the 2 hr mark, Sally ran 16 miles. When Matt goes 40mph, he is approaching Sally at 32mph as she is still running. To go 16 miles at 32mph takes 30 minutes. They meet at 10:30

The algebra way -
Sally is on the line Y=8X where Y is distance and X is the time.
Matt is on the line Y=40X-80 and if you picture this, at the 2 hour mark, he is at zero.
They cross when 40X-80=8X
32X=80
X = 2.5 hours elapsed or 10:30

Note: both ways produce a correct answer. You need to decide when each method is appropriate.
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