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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?

 Aug 15, 2019
 #1
avatar+103122 
+1

Let Kirk's speed  be  R

Let Spock's speed be  R + 30

 

 

So   the time it took  Spock to drive 240 miless  = 240 / (R + 30)

And the time it took Kirk to drive  300 miles  = 300/ R

 

So  twice Spock's time  = Kirk's time  ....so....

 

2 [ 240 ] / ( R + 30)   = 300 / R     simplify

 

480 / (R + 30)  =  300 / R        cross-multiply

 

480 R  = 300 (R + 30)     simplify

 

480 R  =  300R  + 9000         subtract   300R from  both  sides

 

180 R  = 9000        divide  both  sides  by 180

 

R  = 50 mph = Kirk's speed

R + 30  = 80 mph  = Spock's speed

 

And Kirk's time = 300 / R = 300 / 50  = 6 hrs

And Spock's time  = 240 / (50 + 30)   = 240 /  80   =  3 hrs

 

 

cool cool cool

 Aug 15, 2019
 #2
avatar+1342 
+2

Great job CPhill!

tommarvoloriddle  Aug 16, 2019

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