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Tim and lan are 90 miles away from one another. They are

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Tim and lan are 90 miles away from one another. They are  [#permalink]

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New post 07 Sep 2004, 01:32
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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.

will post tye OA later

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New post 07 Sep 2004, 02:01
d) 60 miles.

They would have met up when they had both travelled for 2hrs and 45 mins. In the 2 hr and 45 mins, Tim would have travelled 60miles.
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New post 07 Sep 2004, 02:33
can you please explain how you got 2hrs 45 min
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New post 07 Sep 2004, 02:41
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1. In the 1st hr they would've travelled = 5+10 = 15 miles. So, they are 75 miles apart (90-15 =75) at the end of 1st hour.

2. In the next 1 hour their speeds are 10 +20 = 30 m/hr(relative speed) and hence at the end of the 2nd hour they are 75-30 = 45 miles apart.

3. In the thrid hour their speeds are 20 + 40 = 60m/hr. They would meet each other at 45=60*t => t=3/4 of an hour or 45 minutes.

So, they have met each other end of 2hrs and 45 mins.
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New post 07 Sep 2004, 03:32
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I think there is a quicker way of solving it since the ratio of the starting speed of Tim to that of Elan is 2 : 1.
So even when their speed doubles every one hour their speeds will be in the same ratio. So for an equal time t, we know that the distance covered by Tim and Elan will be corresponding to their speeds.
So Tim travels 2/3 * 90 = 60 miles and Elan travels 30 miles.

Thanks.
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New post 07 Sep 2004, 03:52
venksune wrote:
1. In the 1st hr they would've travelled = 5+10 = 15 miles. So, they are 75 miles apart (90-15 =75) at the end of 1st hour.

2. In the next 1 hour their speeds are 10 +20 = 30 m/hr(relative speed) and hence at the end of the 2nd hour they are 75-30 = 45 miles apart.

3. In the thrid hour their speeds are 20 + 40 = 60m/hr. They would meet each other at 45=60*t => t=3/4 of an hour or 45 minutes.

So, they have met each other end of 2hrs and 45 mins.


i agree with above:
on a different note - if their speeds had remained constant through the journey and we were to find the distance they have travelled when they meet each other:

relative speed = 15mph
distance to cover = 90 miles

so time taken until they meet = 90/15 = 6 hours
so in these 6 hours, Tim would have travelled 60 miles

IF the above is correct - they would meet earlier than 6 hours since now their speeds are doubling by the hour. BUT the distance of 60 miles remains the same - its just covered in less time.

So in the above problem could we use the above logic of 90/15*10 to calc tims distance?

just trying to figure out if my logic is correct.
Thanks!
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Re: Tim and lan are 90 miles away from one another. They are  [#permalink]

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New post 25 Jan 2018, 17:42
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Re: Tim and lan are 90 miles away from one another. They are &nbs [#permalink] 25 Jan 2018, 17:42
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