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Two motorists start a journey at opposite ends of the state and travel

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Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post Updated on: 21 Aug 2017, 04:48
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Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210

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Originally posted by Bunuel on 05 May 2017, 03:53.
Last edited by abhimahna on 21 Aug 2017, 04:48, edited 1 time in total.
Changed "slower than Motorist B " to "slower than Motorist A "
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Re: Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 05 May 2017, 04:09
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I think Bunuel "Motorist B travels at an average rate one-third slower than Motorist B travels" should be replaced with "Motorist B travels at an average rate one-third slower than Motorist A travels". With that assumption:

Speed of A = 375/5 = 75 miles per hour
Speed of B = 1/3 slower than A = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour

Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
Thus, time taken for the two motorists to meet = (relative distance)/(relative speed) = 375/125 = 3 hours
(here relative distance will be taken as complete distance 375 miles - because when they meet together both of them would have covered 375 miles in total)

In 3 hours, A would have covered = 3*75 = 225 miles. Thus C


Alternate:

IF speed of B is 1/3 slower than A, it means speed of B is 2/3 of A. This means ratio of Speed of A:Speed of B = 3:2
Both of them are starting at the same time and when they meet, each of them would have taken the same time to reach that point (obviously). So in the same time, the distances covered are always in the ratio of speeds. So the ratio of distance covered by A: distance covered by B = 3:2

And so when they meet and cover 375 miles in total (distance of A + distance of B equals the length of the road). To find their individual distances covered, we can just divide 375 in the ratio 3:2

Thus distance covered by A = 3/(3+2) * 375 = 225 miles. Thus C
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Re: Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 07 May 2017, 10:45
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Speed of A = 375/5 = 75 miles per hour
Speed of B = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour

Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
time taken to cover the distance = 375/125 = 3 hrs
In 3 hours, A covered = 3*75 = 225 miles.
ANS C
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Re: Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 08 May 2017, 05:29
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Speed of A= \(\frac{375}{5}\)= 75 miles/hr
Speed of B= \(\frac{2}{3}\) of 75= 50 miles/hr

Both of them are moving in opposite direction.

Relative Speed= (75+50)= 125 miles/hr

Time taken to cover the entire distance= \(\frac{375}{125}\)= 3 hrs
Distance covered by A in 3 hrs= 75*3= 225 miles.

Answer: C.

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Re: Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 12 May 2017, 13:21
Bunuel wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist B travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210


We can use the following formula:

distance of A + distance of B = total distance = 375

We are given that the rate of Motorist A is 375/5 = 75 mph and that the rate of Motorist B is 1/3 slower, or 2/3(75) = 50 mph. We can let the time of each motorist = t. Thus:

75t + 50t = 375

125t = 375

t = 3

Thus, Motorist A had driven 75 x 3 = 225 miles when he passed Motorist B’s car.

Answer: C
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Re: Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 01 Oct 2019, 19:22
speed of A ; 375/5 ; 75 mph
speed of B ; 75*2/3 ; 50 mph
total relative speed ; 125 mph
time ; 375/125 ; 3hrs
so Distance of A when it overtakes B ; 3*75 ; 225
IMO C


Bunuel wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210
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Two motorists start a journey at opposite ends of the state and travel  [#permalink]

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New post 02 Oct 2019, 12:30
Bunuel wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210


The two speeds have a direct proportion, the ratio of A's speed to B's is \(1 : \frac{2}{3}\) or \(3:2\). Since they both travel the same amount of time, their distance covered must also have a ratio of \(3:2\). We also know the total distance is 375 miles. Then they will split the 375 miles into 5 equivalent portions, 3 portions belong to A and 2 other portions belong to B. Hence 3/5's of the total distance is traveled by A and the rest by B. \(375 * \frac{3}{5} = 225\).

Ans: C

Once the student masters this ratio method, the only calculation required is 3+2 = 5 then \(375 * \frac{3}{5} = 225\).
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Two motorists start a journey at opposite ends of the state and travel   [#permalink] 02 Oct 2019, 12:30
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