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# A cyclist riding in fog overtakes a man walking...

tagged by: BTGmoderatorLU

### Top Member

#### A cyclist riding in fog overtakes a man walking...

A cyclist riding in fog overtakes a man walking at the speed of 3 km/h. If the man could see the cyclist for 4 minutes an up to a distance of 100m, what is the speed of the cyclist in km/h?

A. 1.5
B. 2.5
C. 4.5
D. 5
E. 6

The OA is C.

I try to solve it as follow,
$$Dist=100m\ =\frac{1}{10}km.$$
$$Time=4\min=\frac{1}{15}hours.$$
$$rate=rate\ of\ cyclits\left(x\right)-rate\ of\ walking=x-3.$$
$$Time=\frac{Dist}{Speed}\ \Rightarrow \frac{\frac{1}{10}}{x-3}=\frac{1}{15}\ \Rightarrow x=4.5\.$$

### GMAT/MBA Expert

Senior | Next Rank: 100 Posts
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LUANDATO wrote:
A cyclist riding in fog overtakes a man walking at the speed of 3 km/h. If the man could see the cyclist for 4 minutes an up to a distance of 100m, what is the speed of the cyclist in km/h?

A. 1.5
B. 2.5
C. 4.5
D. 5
E. 6

The OA is C.

I try to solve it as follow,
$$Dist=100m\ =\frac{1}{10}km.$$
$$Time=4\min=\frac{1}{15}hours.$$
$$rate=rate\ of\ cyclits\left(x\right)-rate\ of\ walking=x-3.$$
$$Time=\frac{Dist}{Speed}\ \Rightarrow \frac{\frac{1}{10}}{x-3}=\frac{1}{15}\ \Rightarrow x=4.5\.$$
Absolutely perfect - love the way to set up the parameters, wrote down your equation given the speed of the walker and derived the solution. I would have done it in the same way.

As a challenge, what would be the answer if the person is walking towards the cyclist as opposed to the same direction?

### Top Member

Legendary Member
Joined
29 Oct 2017
Posted:
571 messages
Followed by:
4 members
Hi,

In 4 minutes, the cyclist gains 100m on the person walking.

So let's see how much does the man travel in 4 minutes at 3 km/h = (3000/60)*4 = 200m.

If the man has traveled 200m, then the cyclist travels = 200m + 100m = 300m.

So, his speed = (300/4)*(60/1000) = 4.5 km/h. Option C.

Regards!

### GMAT/MBA Expert

GMAT Instructor
Joined
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Posted:
1461 messages
Followed by:
16 members
39
LUANDATO wrote:
A cyclist riding in fog overtakes a man walking at the speed of 3 km/h. If the man could see the cyclist for 4 minutes an up to a distance of 100m, what is the speed of the cyclist in km/h?

A. 1.5
B. 2.5
C. 4.5
D. 5
E. 6
We see that the rate of the cyclist exceeds the rate of the man by 100 m in 4 minutes, or 25 m/min. We need to convert this into km/h:

25 m/min x 1 km/1000 m x 60 min/h = 1500/1000 km/h = 1.5 km/h

If we let r = the rate of the cyclist in km/h, then

r - 3 = 1.5

r = 4.5

_________________
Jeffrey Miller Head of GMAT Instruction

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