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,
$$Dist=100m\ =\frac{1}{10}km.$$
$$Time=4\min=\frac{1}{15}hours.$$
$$rate=rate\ of\ cyclits\left(x\right)-rate\ of\ walking=x-3.$$
$$Time=\frac{Dist}{Speed}\ \Rightarrow \frac{\frac{1}{10}}{x-3}=\frac{1}{15}\ \Rightarrow x=4.5\.$$
Experts, any suggestion about this PS question? Thanks in advance.
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A cyclist riding in fog overtakes a man walking...
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BTGmoderatorLU
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mbawisdom
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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.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,
$$Dist=100m\ =\frac{1}{10}km.$$
$$Time=4\min=\frac{1}{15}hours.$$
$$rate=rate\ of\ cyclits\left(x\right)-rate\ of\ walking=x-3.$$
$$Time=\frac{Dist}{Speed}\ \Rightarrow \frac{\frac{1}{10}}{x-3}=\frac{1}{15}\ \Rightarrow x=4.5\.$$
Experts, any suggestion about this PS question? Thanks in advance.
As a challenge, what would be the answer if the person is walking towards the cyclist as opposed to the same direction?
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!
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!
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Jeff@TargetTestPrep
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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: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
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
Answer: C
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