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09 Oct 2023, 21:43
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Difficulty:
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Question Stats:
79% (02:43) correct
21%
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On a 1-mile test course, a vehicle is travelling at a constant rate of r miles per hour. If it were traveling at a rate of r+20 miles per hour, it would take 4 min less time to travel the test course. What is the value of r?
A. 5
B. 10
C. 20
D. 25
E. 30
2024-01-24_19-31-47.png [ 36.33 KiB | Viewed 18374 times ]
A. 5
B. 10
C. 20
D. 25
E. 30
Attachment:
2024-01-24_19-31-47.png [ 36.33 KiB | Viewed 18374 times ]
Updated on: 11 Jul 2024, 05:26
Originally posted by MartyMurray on 29 Feb 2024, 19:56.
Last edited by MartyMurray on 11 Jul 2024, 05:26, edited 1 time in total.
Last edited by MartyMurray on 11 Jul 2024, 05:26, edited 1 time in total.
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On a 1-mile test course, a vehicle is travelling at a constant rate of r miles per hour. If it were traveling at a rate of r+20 miles per hour, it would take 4 min less time to travel the test course. What is the value of r?
A. 5
B. 10
C. 20
D. 25
E. 30
We can quickly solve this one by checking the answer choices.
The car is going around a 1-mile course.
At 20 miles per hour, the car would go around the course in 3 minutes since 60/20 is 3 minutes.
Thus, r can't be 20, 25, or 30 miles per hour since, in each of those case, the car would go around the track in less than 4 minutes at r. So, there's no way for it to take 4 minutes less to go around the track at r + 20.
So, 10 and 5 are the only possible options.
Check 10.
At 10 miles per hour, a car goes a mile every 60/10 = 6 minutes.
At 10 + 20 = 30 miles per hour, a car goes a mile every 60/30 = 2 minutes.
6 - 2 = 4
Correct answer: B
A. 5
B. 10
C. 20
D. 25
E. 30
We can quickly solve this one by checking the answer choices.
The car is going around a 1-mile course.
At 20 miles per hour, the car would go around the course in 3 minutes since 60/20 is 3 minutes.
Thus, r can't be 20, 25, or 30 miles per hour since, in each of those case, the car would go around the track in less than 4 minutes at r. So, there's no way for it to take 4 minutes less to go around the track at r + 20.
So, 10 and 5 are the only possible options.
Check 10.
At 10 miles per hour, a car goes a mile every 60/10 = 6 minutes.
At 10 + 20 = 30 miles per hour, a car goes a mile every 60/30 = 2 minutes.
6 - 2 = 4
Correct answer: B
09 Oct 2023, 22:07
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nick13
Given
\(\frac{1}{r} - \frac{1}{r+20} = \frac{4}{60}\)
Taking the denominator as \(r(r+20)\)
\(r + 20 - \frac{r}{r(r+20)} = \frac{1}{15}\)
\(20 * 15 = r(r+20)\)
\(300 = r(r+20)\)
Answer choice elimination
A. \(5 → 5(5+20) = 5 * 25 \neq 300\) ⇒ Eliminate
B. \(10 → 10(10+20) = 10 * 30 = 300 \) ⇒Keep
Option B
