Renee just got on the freeway to go to her cousin's house in Denver. She is driving 50 miles per hour. Her sister Kim left one hour after her. She got on the same freeway, and she is driving 60 miles per hour. How long will it take Kim to catch up to Renee?

let's say they catch-up to each other after t hour.

so

in t hour distance travelled by Renee

d = speed * time = 50t

in t hour distance travelled by Kim

d = speed * time = 60 (t-1) + 0*1 = 60 (t-1)

Note: here kim didn't covered any distance in first hour and in rest t-1 hour it travelled all distance

now. as distance travelled by both is same so

60 (t-1) = 50t

60t - 60 = 50t

adding 60 both sides

60t = 50t+60

subtracting 50t both sides

60t - 50t = 50t+60 - 50t

10t = 60

dividing by 10 both sides

t = 60/10 = 6

so in 6 hour both will catch-up to each other