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guddo
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The distance between Town R and Town S is 209 miles. At noon 27 Nov 2023, 09:47
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The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

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Bunuel
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The distance between Town R and Town S is 209 miles. At noon 27 Nov 2023, 10:22
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guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114
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The combined speed of the motorists is 40 + 55 = 95 miles per hour. Thus, they would meet after (time) = (distance)/(combined speed) = 209/95 hours. Therefore, the distance from Town R at which they would meet is (distance) = (time)*(speed of the motorist from R) = 209/95*40 = 209/19*8 = 11*8 = 88 miles."

Answer: B.
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The distance between Town R and Town S is 209 miles. At noon 27 Nov 2023, 14:19
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guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114
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The ratio of distance covered will be the equal ratio of the speed

Ratio of distance covered = \(\frac{40}{55} = \frac{8}{11}\)

Hence, out of 19 parts, the motorist who started from Town R covers \(8\) parts and the motorist who started from Town S covers \(11\) parts.

Distance from Town R = \(\frac{209}{19} * 8 = 88\) miles

Option B
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The distance between Town R and Town S is 209 miles. At noon 27 Nov 2023, 10:55
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relative speed when moving in opposite direction 95miles
time they meet will be 209/95 ; 2.2
distance covered by motorist in 2.2 hours
2.2*40 ; 88
option B

guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114
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The distance between Town R and Town S is 209 miles. At noon 20 Aug 2024, 03:45
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As both used the same time until they meet, we know that both together will drive the distance of 209. Hence, 40t=209-55t => t=209/95. We now have to multiply the time with the speed of 40 m/h as we are interested in the distance that was driven starting in R. Dr=209*40/95=88, choice B.­
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The distance between Town R and Town S is 209 miles. At noon 06 Sep 2024, 11:00
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­Without doing any math, you can guess the correct answer using the following logic:

1) Given the numbers in the prompt: 209, 40, and 55, it's unlikely that the resulting answer will be an answer that ends in 0 or 5. Therefore, you can eliminate 80,95 and 100, leaving 88 or 114.

2) After 2 hours, Motorist 1 will have traveled 80 miles, and Motorist 2 will have traveled 110 miles (approx. 100 miles from Town R), yet they still have not crossed paths. Therefore, you can eliminate 114, and choose 88.­
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The distance between Town R and Town S is 209 miles. At noon 17 Nov 2024, 13:15
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why do we use speed of R instead of 55mph?
Bunuel
guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

The combined speed of the motorists is 40 + 55 = 95 miles per hour. Thus, they would meet after (time) = (distance)/(combined speed) = 209/95 hours. Therefore, the distance from Town R at which they would meet is (distance) = (time)*(speed of the motorist from R) = 209/95*40 = 209/19*8 = 11*8 = 88 miles."

Answer: B.
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The distance between Town R and Town S is 209 miles. At noon 17 Nov 2024, 13:31
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micahman
why do we use speed of R instead of 55mph?
Bunuel
guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

The combined speed of the motorists is 40 + 55 = 95 miles per hour. Thus, they would meet after (time) = (distance)/(combined speed) = 209/95 hours. Therefore, the distance from Town R at which they would meet is (distance) = (time)*(speed of the motorist from R) = 209/95*40 = 209/19*8 = 11*8 = 88 miles."

Answer: B.
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We need the distance from Town R, so we multiply the time until the meeting point by the speed of the motorist from R. If we multiplied by the speed of the motorist from S, we’d get the distance from Town S instead. Essentially, the distance from R is the distance the motorist from R drove to reach the meeting point.
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The distance between Town R and Town S is 209 miles. At noon 18 Apr 2025, 23:31
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Is this method valid

time is equal so

40d = 55(209-d)
deduced to
d = 121 (Motorist 1)
d = 88 (Motorist 2 )
lower of the 2 is the distance passed when they met.
Bunuel
guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

The combined speed of the motorists is 40 + 55 = 95 miles per hour. Thus, they would meet after (time) = (distance)/(combined speed) = 209/95 hours. Therefore, the distance from Town R at which they would meet is (distance) = (time)*(speed of the motorist from R) = 209/95*40 = 209/19*8 = 11*8 = 88 miles."

Answer: B.
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The distance between Town R and Town S is 209 miles. At noon 19 Apr 2025, 00:43
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guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

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2023-11-27_20-30-47.png
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One way to do this would be to add the speeds of both motorists and figure out how much time it would take to cover the total distance. That time is when the two motorists would pass each other.

(Distance / Speed) = Time

(209 miles / 95 mph) = (209 / 95) hours

Multiply the hours by the speed of the motorist starting from Town R.

(209 / 95) hours x (40) mph = 88 miles

(B) is your answer.
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The distance between Town R and Town S is 209 miles. At noon 19 Apr 2025, 02:34
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rak08
Is this method valid

time is equal so

40d = 55(209-d)
deduced to
d = 121 (Motorist 1)
d = 88 (Motorist 2 )
lower of the 2 is the distance passed when they met.
Bunuel
guddo
The distance between Town R and Town S is 209 miles. At noon yesterday, a motorist started from Town R and drove to Town S at a constant speed of 40 miles per hour, and another motorist started from Town S and drove along the same route to Town R at a constant speed of 55 miles per hour. What was the motorists' distance, in miles, from Town R when they passed each other?

A. 80
B. 88
C. 95
D. 100
E. 114

The combined speed of the motorists is 40 + 55 = 95 miles per hour. Thus, they would meet after (time) = (distance)/(combined speed) = 209/95 hours. Therefore, the distance from Town R at which they would meet is (distance) = (time)*(speed of the motorist from R) = 209/95*40 = 209/19*8 = 11*8 = 88 miles."

Answer: B.
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Yes, your method is valid, but since the question asks for the distance from Town R, it’s cleaner to let that distance be d from the start. Then set up the equation d/40 = (209 - d)/55. Solving this gives d = 88 directly, which is the distance from Town R when they meet.
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