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# Two cyclists start biking from a trails start 3 hours apart.

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Manager
Joined: 03 Jul 2005
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Two cyclists start biking from a trails start 3 hours apart. [#permalink]  12 Dec 2006, 22:47
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Two cyclists start biking from a trailâ€™s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

a) 2 hours
b) 4 Â½ hours
c) 5 Â¾ hours
d) 6 hours
e) 7 Â½ hours
Director
Joined: 05 Feb 2006
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Re: PS: Cyclist [#permalink]  12 Dec 2006, 23:22
lfox2 wrote:
Two cyclists start biking from a trailâ€™s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

a) 2 hours
b) 4 Â½ hours
c) 5 Â¾ hours
d) 6 hours
e) 7 Â½ hours

A bit unclear question... what exactly does this "3 hours apart" means...

It is written that the second cyclist starts 3 hours after the first, so is this the repeated info or not? if yes, the answer is 4.5 hours.

A: rate=10/1.....t=t.....d=d
B: rate=6/1.......t=t+3 (started 3 hours earlier).....d=d

Construct two equations:

10t=d
6t+18=d....merge

6t+18=10t
-4t=-18
t=4.5 hours....

But the question is bit unclear to me.....
Senior Manager
Joined: 20 Feb 2006
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[#permalink]  13 Dec 2006, 12:42
1st cyclist travels 3*6=18miles when the second cyclist starts.

Closing speed of second cyclist = 10-6=4mph

Time until they meet = 18/4 = 4.5 hrs
Director
Joined: 06 Sep 2006
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[#permalink]  13 Dec 2006, 12:58
first cyclist travels 6*3 = 18 miles before the second one starts paddling.

If 'S' is the distance first cyclist cover before the second catches up

Time it takes the first one to get to distance S, t = S/6

Time it takes the second one to get to the same distance = (S + 18)/10

since two takes the same time:

S/6 = (S + 18)/10

3 * 18 + 3S = 5S
S = 27

time = 27/6 = 4.5
[#permalink] 13 Dec 2006, 12:58
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# Two cyclists start biking from a trails start 3 hours apart.

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