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25 Aug 2021, 10:09
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In a 60-mile trip, the first 30 miles took 40 minutes. The average speed for the entire trip
was 54 mph. What is the speed in miles per hour of the last 30 miles?
a. 58.5 mph b. 60.5 mph c. 62 mph d. 67.5 mph
was 54 mph. What is the speed in miles per hour of the last 30 miles?
a. 58.5 mph b. 60.5 mph c. 62 mph d. 67.5 mph
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DashingNightmare2
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Joined: 30 May 2021
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25 Aug 2021, 10:29
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Average speed =\(\frac{ total distance }{ total time}\)
Total distance =60 miles
Average speed =54 mph
Total time = \(\frac{60}{54}\) =\(\frac{10}{9}\) hr
Total time =\(\frac{ 10}{9 }\) = \(\frac{40}{60}\) + t (t is the time of 2nd half)
=>\(\frac{ 10}{9 }\) =\(\frac{ 2}{3 }\)+t
=> t = \(\frac{4}{9}\)
speed in miles per hour of the last 30 miles = \(\frac{30}{4/9}\) =67.5
hence IMO D
Total distance =60 miles
Average speed =54 mph
Total time = \(\frac{60}{54}\) =\(\frac{10}{9}\) hr
Total time =\(\frac{ 10}{9 }\) = \(\frac{40}{60}\) + t (t is the time of 2nd half)
=>\(\frac{ 10}{9 }\) =\(\frac{ 2}{3 }\)+t
=> t = \(\frac{4}{9}\)
speed in miles per hour of the last 30 miles = \(\frac{30}{4/9}\) =67.5
hence IMO D
25 Aug 2021, 10:29
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Over the course of a Journey, in which the 2 parts traveled are of equal Distance, the Average Speed is the Harmonic Mean of the 2 speeds traveled at during the 2 equal distance Parts.
In other Words:
Let Speed traveled at over the 1st 30 miles = A m/h
Let Speed traveled at over the 2nd 30 miles = B m/h
Let the Average Speed = S
since each part of the journey is of equal distance (30 miles), the Average Speed is found by the Formula:
S = (2*A*B) / (A + B)
we are given the Overall Average Speed = 54 mph = S
A: the first 30 miles are covered in 40 minutes ------> (40/60) of an hour ------> (2/3) of an hour
A = Speed over first 30 miles = (30) / (2/3) = (3 * 30) / (2) = 45 mph
What is B = speed over the last 30 miles = ?
Substitute: S = 54 ---- and ----- A = 45
54 = (2*45*B) / (45 + B)
----cancel a Factor of 18 from the NUM on each side of the Equation---
3 = (5*B) / (45 + B)
135 + 3B = 5B
135 = 2B
B = 67.5
Answer: 67.5 mph
In other Words:
Let Speed traveled at over the 1st 30 miles = A m/h
Let Speed traveled at over the 2nd 30 miles = B m/h
Let the Average Speed = S
since each part of the journey is of equal distance (30 miles), the Average Speed is found by the Formula:
S = (2*A*B) / (A + B)
we are given the Overall Average Speed = 54 mph = S
A: the first 30 miles are covered in 40 minutes ------> (40/60) of an hour ------> (2/3) of an hour
A = Speed over first 30 miles = (30) / (2/3) = (3 * 30) / (2) = 45 mph
What is B = speed over the last 30 miles = ?
Substitute: S = 54 ---- and ----- A = 45
54 = (2*45*B) / (45 + B)
----cancel a Factor of 18 from the NUM on each side of the Equation---
3 = (5*B) / (45 + B)
135 + 3B = 5B
135 = 2B
B = 67.5
Answer: 67.5 mph
