SOLUTION: It takes Bob the same amount of time to travel 600 miles as it takes Kurt to travel 450 miles. If Bob drives 20mph faster than Kurt, how fast does each person drive?

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Question 62274: It takes Bob the same amount of time to travel 600 miles as it takes Kurt to travel 450 miles. If Bob drives 20mph faster than Kurt, how fast does each person drive?
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
It takes Bob the same amount of time to travel 600 miles as it takes Kurt to travel 450 miles. If Bob drives 20mph faster than Kurt, how fast does each person drive?
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Bob DATA:
distance = 600 miles ; rate=x mph ; time=d/r=600/x
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Kurt DATA:
distance = 450 miles ; rate = x-20 mph ; time = d/r = 450/(x-20)
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EQUATION:
time = time
600/x = 450/(x-20)
12/x = 9/(x-20)
12x-240 = 9x
3x=240
x=80 mph (Bob's rate)
x-20=60 mph (Kurt's rate)
Cheers,
Stan H.

Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website!
Distance = (Rate)(Time) [use the distance formula]
Bob: 600=(r+20)t
Solve for t: 600/(r+20)=t
.
Kurt: 450=rt
Solve for t:450/r=t
.
Bob's time = Kurt's time
So, 600/(r+20)=450/r[Solve for r]
(600)(r)=(r+20)(450)
600r=450r+9000
600r-450r=9000
150r=9000
r=9000/150
r=60 miles per hour
.
Kurt=r=60 miles per hour
Bob: r+20=60+20=80 miles per hour