Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
Select the correct option.
A) 30 miles .  B) 35 miles .  C) 45 miles .  D) 60 miles .  E) 65 miles .

Rationale: "in 1 st hour : relative speed of the two will be 10 + 5 = 15 miles / hour . as they move towards each other , the distance between them reduces by 15 miles . distance left between them : 90 - 15 = 75 miles . in 2 nd hour : speed of tim : 20 mph , that of elan : 10 mph . relative speed of the two will be 20 + 10 = 30 miles / hour . as they move towards each other , the distance between them reduces by 30 miles . distance left between them : 75 - 30 = 45 miles . in 3 rd hour : speed of tim : 40 mph , that of elan : 20 mph . relative speed of the two will be 40 + 20 = 60 miles / hour . now in order to cover the remaining distance of 45 miles . they will take : ( 45 / 60 ) hrs . = ( 3 / 4 ) hour . distance travelled by tim ? in first hour : 1 hour * ( 10 miles per hour ) = 10 miles in second hour : 1 hour * ( 20 miles per hour ) = 20 miles in third hour : ( 3 / 4 ) hour * ( 40 miles per hour ) = 30 miles total distance travelled : 10 + 20 + 30 = 60 miles . d is the answer"
Answer: D