For these problems, I like to simplify a little bit. We know the speed is going to be changing, but since they keep the same speed over the course of each hour, they will meet while going at constant speed.

At the beginning they are 90 miles apart. Tim is at mile 0 and Elan is at mile 90.

After 1 hour, Tim travels 10 miles (10 mph) to mile 10 and Elan travels 5 miles (5 mph) to mile 85. They are now 75 miles apart.

Their speed doubles, so Tim travels 20 mph in mile 2 and Elan travels 10 mph. After 2 hours, Tim travels 20 miles (20 mph) to mile 30 and Elan travels 10 miles (10 mph) to mile 75. They are now 55 miles apart.

Their speed doubles again, so Tim is now traveling 40 mph in mile 3 and Elan travels 20 mph. We can see that they will meet during this hour because they only have 45 miles between them and they will travel a total of 60 miles (40 + 20 mph). We can add their speeds together to find a cumulative speed of 60 mph. Since they are 45 miles apart, we know they will meet after 45 minutes. If Tim travels 40 mph, he will travel 30 miles in the 45 minutes and will be at mile 60 when they meet.

D

nidhis.1408 wrote: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?
(a) 30 miles. (b) 35 miles. (c) 45 miles. (d) 60 miles. (e) 65 miles.

Since the ratio of their speeds are not changing throughout their travel, the ratio of their distances travelled as well will not change in given time.
so Tim will travel 60 miles before he meets Elan.

is it D?

Yes the answer is D but i still didn't follow the ratio approach.

nidhis.1408 wrote:Yes the answer is D but i still didn't follow the ratio approach.

User123321 - that's a great approach. I didn't think about that.

What he is saying here is that the ratio of Tim's speed to Elan's speed always stays the same at 2:1. Tim will always be moving at a speed double that of Elan's. He starts out at 10 mph while Elan is at 5 mph. He is then at 20 mph while Elan is at 10 mph. And so on.

So Tim will also cover 2x the distance. Since the original distance apart is 90 miles, Tim will cover 60 miles during the same time Elan will cover 30.

oh dats neat! finally got it. thanks:)

IMO: D

nidhis.1408 wrote: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?
(a) 30 miles. (b) 35 miles. (c) 45 miles. (d) 60 miles. (e) 65 miles.

Almost no math is needed here.

Tim = 10mph, Elan = 5mph.
Even when they start to double their respective rates, in each case, Tim will travel TWICE AS FAST as Elan.
Thus, Tim must travel TWICE THE DISTANCE traveled by Elan.
Only answer choice D works:
Tim = 60, implying that Elan = 30.

The correct answer is D.