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?

Guest Aug 15, 2019

#1**+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

CPhill Aug 15, 2019