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18 Mar 2019, 03:51
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Difficulty:
35%
(medium)
Question Stats:
74% (02:44) correct
26%
(02:00)
wrong
based on 98
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Mr. Earl E. Bird gets up every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time?
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
18 Mar 2019, 04:00
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Bunuel
Mr. Earl E. Bird gets up every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time?
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
avg speed = 2*a*b/a+b
2*40*60 /100
IMO B 48
06 Apr 2020, 03:54
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Bunuel
Mr. Earl E. Bird gets up every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time?
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
(A) 45
(B) 48
(C) 50
(D) 55
(E) 58
Solution:
Let x and t be the distance between home and office, and usual time of Mr. Bird, respectively.
- • We know that distance well remain same
- o \(Distance = Speed*time\)
- Distance = \(40*(t + 3)\)…(i)
Distance = \(60*(t - 3)\)…(ii)
- o \(40*(t+3) = 60*(t-3)\)
o \(2*(t+3) = 3*(t-3)\)
o \(2t + 6 = 3t – 9\)
o \(6+9 = 3t – 2t\)
o \(15 = t\)
• Required speed = \(\frac{720}{15} =48\) Miles per hour
Alternative method
We can also find the answer by using the concept of average speed.
- • We can use average speed because the when speed is 40 time is t + 3 and when speed is 60 time is t - 3, it means they are equidistant from t on the number line
• If a and b be the speed while going and returning back through the same path
- o Then average speed = \(2a*b(a + b)\) [Note: average speed will not be arithmetic mean of the speeds]
- Required speed = \(\frac{2*40*60}{100} = 48\) miles per hour
