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# Two motorists start a journey at opposite ends of the state

tagged by: BTGmoderatorLU

### Top Member

#### Two motorists start a journey at opposite ends of the state

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 OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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LUANDATO 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
When A and B travel toward each other, they WORK TOGETHER to cover the 375 miles between them.

Motorist B travels at an average rate one-third slower than Motorist A travels.
If A's rate = 3 miles per hour, then B's rate = 3 - (1/3)3 = 3-1 = 2 miles per hour.
Implication:
Of every 5 miles traveled when A and B work together, A travels 3 miles, while B travels 2 miles.
Thus, A will travel 3/5 of the 375-mile distance:
(3/5)(375) = (3)(75) = 225 miles.

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LUANDATO 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
Two motorists, A and B, starting a trip at opposite ends of a 375-mile road meet somewhere on that road. Thus, we know that the sum of the distances that their two cars have traveled will equal 375 miles. We can summarize this with the following equation:
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 travel 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.

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Hi LUANDATO,

Also, you can solve this question as follow,

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 oppositive directions, their relative speed = (75 + 50) = 125 miles per hour.

The time taken to cover the distance = 275 / 125 = 3 hours.

In 3 hours, A covered = 3 * 75 = 225 miles. Option C.

Regards!

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