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# Two cyclists start from the same place to ride in the same direction.

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Re: Two cyclists start from the same place to ride in the same direction. [#permalink]
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Bunuel wrote:
Two cyclists start from the same place to ride in the same direction. A starts at noon at 8 kmph while B starts at 2 pm at the rate of 10 kmph. How far will A have ridden before he is overtaken by B?

A. 75 km
B. 76 km
C. 78 km
D. 80 km
E. 84 km

Solution:

If we let t = the time ridden by B, then (t + 2) = the time ridden by A, and we can create the equation:

8(t + 2) = 10t

8t + 16 = 10t

16 = 2t

8 = t

So A will have ridden 8 x (8 + 2) = 8 x 10 = 80 km before being overtaken.

Alternate Solution:

At 2 PM, A has been traveling for 2 hours; thus, A is 2 * 8 = 16 km from the starting point.

Since B is 10 - 8 = 2 km/h faster than A, it will take B 16/2 = 8 hours to catch up with A. So, B will overtake A at 2 PM + 8 hours = 10 PM.

At 10 PM, A has been traveling for 10 hours; thus, A will have traveled 8 x 10 = 80 km before being overtaken.

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Re: Two cyclists start from the same place to ride in the same direction. [#permalink]
Bunuel wrote:
Two cyclists start from the same place to ride in the same direction. A starts at noon at 8 kmph while B starts at 2 pm at the rate of 10 kmph. How far will A have ridden before he is overtaken by B?

A. 75 km
B. 76 km
C. 78 km
D. 80 km
E. 84 km

Are You Up For the Challenge: 700 Level Questions

|Cyclist| Time | Speed |
--------------------------
| A |12:00 | 8kph |
| B |02:00 | 10kph |
--------------------------
Diff |02hrs | 2kph |
---------------------------
Dist A: 8kph * 2hrs = 16km
Time B: 16km / 10kph= 8hrs
Dist A before B catches up = (8hrs + 2hrs) * 8kph = 80km­
Re: Two cyclists start from the same place to ride in the same direction. [#permalink]
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