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A man travels from City A to City B at 60 miles/hr,

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A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 10 Aug 2018, 09:56
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Question Stats:

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A man travels from City A to City B at 60 miles/hr, and returns to city A at 40 miles/hr. If the entire journey took 10 hrs in all then what is the distance between City A and City B?
(A)120
(B)240
(C)272
(D)280
(E)288
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A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 10 Aug 2018, 16:00
Probus wrote:
A man travels from City A to City B at 60 miles/hr, and returns to city A at 40 miles/hr. If the entire journey took 10 hrs in all then what is the distance between City A and City B?
(A)120
(B)240
(C)272
(D)280
(E)288

The trap answer is A. Total time represents time for the round trip = 2D. No need to divide by 2.

At one rate, HALF the round-trip distance took = \(\frac{D}{60}\) hours

And at another rate, the other HALF of the trip took \(\frac{D}{40}\) hours.
Total distance in the sum of hours = 2D

Time from A to B: \(\frac{D}{r}=\frac{D}{60}\)

Time from B to A \(=\frac{D}{40}\)

Those two times sum to 10 hours

\((\frac{D}{60}+\frac{D}{40})=10\)
Multiply all terms by LCM = 120
\(2D+3D=1,200\)
\(5D=1,200\)
\(D=240\)

Answer B
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Re: A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 10 Aug 2018, 21:39
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Probus wrote:
A man travels from City A to City B at 60 miles/hr, and returns to city A at 40 miles/hr. If the entire journey took 10 hrs in all then what is the distance between City A and City B?
(A)120
(B)240
(C)272
(D)280
(E)288


Total distance covered=AB+BA=2*AB
Total time taken=10 hours
Average speed=Total distance/Total time
So, Total distance=2*AB=Average speed*10

Question stem:- AB=?

Average speed
=\(\frac{2v_{1}*v_{2}}{v_{1}+v_{2}}\)
Note:- Applicable when the distance covered at two speeds is same (here distance AB covered at 60 mph and distance BA covered at 40 mph, AB=BA)

So, average speed=\(\frac{2*60*40}{60+40}\)=48 mph

We have, 2*AB=48*10
Or, AB=240 miles

Ans. (B)
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Re: A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 10 Aug 2018, 23:51
Let D= distance between City A and City B

\(\frac{D}{60}\)+\(\frac{D}{40}\)= 8

Plug in Value of option B. It satisfies the above equation.

Answer: B.
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Re: A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 10 Aug 2018, 23:54
Probus wrote:
A man travels from City A to City B at 60 miles/hr, and returns to city A at 40 miles/hr. If the entire journey took 10 hrs in all then what is the distance between City A and City B?
(A)120
(B)240
(C)272
(D)280
(E)288

Distance is given in the options, IMHO the best approach will be using the options twice with speeds 60 and 40, adding up to 10..

Answer must be (B)

\(\frac{240}{60} + \frac{240}{40} = 4 + 6 => 10\)
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Re: A man travels from City A to City B at 60 miles/hr,  [#permalink]

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New post 18 Aug 2018, 19:09
Probus wrote:
A man travels from City A to City B at 60 miles/hr, and returns to city A at 40 miles/hr. If the entire journey took 10 hrs in all then what is the distance between City A and City B?
(A)120
(B)240
(C)272
(D)280
(E)288


Let d = the distance between City A to City B. So we have the following equation for the time:

Time from A to B + Time from B back to A = 10 hours

d/60 + d/40 = 10

Multiplying both sides of the equation by 240, we have:

4d + 6d = 2400

10d = 2400

d = 240

Answer: B
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Re: A man travels from City A to City B at 60 miles/hr, &nbs [#permalink] 18 Aug 2018, 19:09
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