SOLUTION: 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?

Algebra ->  Length-and-distance -> SOLUTION: 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?      Log On


   

Question 1143969: 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?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the Kirk' speed, in miles per hour.


Then the Spock' speed is (x+30) mph.


The time for Kirk is  300%2Fx hours.


The time for Spock is  240%2F%28x%2B30%29 mph.


The time equation is


    300%2Fx = 2%2A%28240%2F%28x%2B30%29%29.


From this equation,


    300*(x+30) = 480x,

    300x + 9000 = 480x

    9000 = 480x - 300x

    9000 = 180x

    x = 9000%2F180 = 50.


ANSWER.  Kirk' speed is  50 mph;  Spock' speed is 50+30 = 80 mph.

                Kirk's time is  300%2F50 = 6 hours;  Spock' speed is  240%2F80 = 3 hours.

Solved.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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