SOLUTION: Amadeus could travel 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. If Amadeus's rate exceeded that of Salieri by 40 miles per hour, find the rates an

Question 1144049: Amadeus could travel 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. If Amadeus's rate exceeded that of Salieri by 40 miles per hour, find the rates and times of both men.
Found 3 solutions by Alan3354, josgarithmetic, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Same problem, different numbers.
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Kirk could drive 300 miles in twice the time it took Spock to drive 240 miles. The speed of Spock was 30 mph greater than that of Kirk. What were the speed and times of both?
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K = Kirk's speed
S = Spock's speed = (K+30)
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t = Spock's time to go 240 miles
2t = Kirk's time to go 300 miles
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150/K = 240/S = 240/(K+30)
Invert
K/150 = (K+30)/240
K/5 = (K+30)/8
8K = 5K+150
K = 50 mi/hr
S = 80 mi/hr
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
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Amadeus could travel 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. If Amadeus's rate exceeded that of Salieri by 40 miles per hour, find the rates and times of both men.
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Amadeus could travel D miles in twice the time it took his nemesis Salieri to travel d miles. If Amadeus's rate exceeded that of Salieri by k miles per hour, find the rates and times of both men.
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SPEED TIME DISTANCE Amadeus r+k D/(r+k) D Salieri r d/r d D=760 d=220 k=40

The first sentence of the description means ;
the only UNKNOWN in this equation is r. Solve for r.
Evaluate r+k.
Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

Amadeus could travel 760 miles in twice the time it took his nemesis Salieri to travel 220 miles.

So Amadeus could travel 760/2 = 380 miles in the SAME amount of time.

In the same amount of time, Amadeus could travel 380-220 = 160 miles farther.

160 miles difference in distances, with a difference of 40 mph in their speeds, means a travel time of 160/40 = 4 hours.

So Amadeus can travel 380 miles in 4 hours, a speed of 380/4 = 95mph; Salieri can travel 220 miles in 4 hours, a speed of 220/4 = 55mph.
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