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?
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