Tim and Élan are 90 miles away from one another. They are starting to

In 1st 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 2nd hour: Speed of Tim: 20Mph, 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 3rd 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.

Since they are travelling towards each other the speed needs to abe added !!

Distance = 90 miles
first hour !!
total distance travelled = 10+5=15 miles
distance left = 90-15 =75 miles
second hour !!
total distance travelled = 20+10=30 miles (speed doubles)
distance left = 75-30=45 miles
third hour !!
total distance travelled = 40+20=60 miles
since distance left is only 45 miles
time taken to complete 45 miles = 45/60 = 3/4 hour
in this period , distance travelled by tim = (3/4)*40=30 miles
Total distance travelled by tim = 10 + 20 + 30 = 60 miles

Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.

Plugging in the answer choice Only Answer Choice D meet the 2:1(Tim:Elan=60:30) ratio of maintaining total distance traveled 90 miles


So Correct answer D

I solved it with this logic. A little visually though:
------>Tim: 10,20,40,80,160 (we consider only upto 80 as beyond that no point doubling speed)
80,40,20 ,10,5 <-------
we see the overlap in terms of 40 mph and 20 mph
20 we can discard Elan would be too far even if he doubled his speed, 80 would mean Tim overshot Elan
with regard to 40, we do 90/40 --> 9/4. If we divide 90 into 4 parts we get approx 25/25/25/25 (les than 100 though). 9/4 ~ 3/2 which is then 3 parts out 2; approximately 60 (it has to be more than 45 but less than 65)

Tim's disatnce after 3.5 hrs is 60 miles
Elan's distance after 3.5 hrs is 30 miles.

Answer D

While the ratio method works absolutely fine there are times when one can't think of such elegant answers.

The easier way to do it is a make a table

Distance Tim Elan
1st Hour 10 5
2nd Hour 20 10
3rd Hour 40 20
3 1/2 Hours 60 30

Hence at 3 1/2 hours Tim meets Elan and has covered 60 Miles.
Answer D

If this answer helped you a kudos is appreciated.

After 2 hours Tim covers 30 miles and Elan covers 15 miles.

Since ratio of their speeds is 2:1

30 + 2x + 15 + x = 90

3x = 45

x = 15

Therefore distance Tim covers =

30 + 2(15) = 60 miles.

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