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14 Jul 2017, 09:47
Kudos
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Let the total distance between A and B be \(d\), and \(s\) be the speed.
\(\frac{d}{2*90} + \frac{d}{2*s} = \frac{d}{60}\)
\(\frac{d}{180} + \frac{d}{2s} = \frac{d}{60}\)
\(\frac{d}{2}(\frac{1}{90} + \frac{1}{s}) = \frac{d}{2}(\frac{1}{30})\)
\(\frac{1}{s} = \frac{1}{30} - \frac{1}{90} = \frac{60}{2700} = \frac{2}{90}\)
\(s = \frac{90}{2} = 45.\) Ans - B.
\(\frac{d}{2*90} + \frac{d}{2*s} = \frac{d}{60}\)
\(\frac{d}{180} + \frac{d}{2s} = \frac{d}{60}\)
\(\frac{d}{2}(\frac{1}{90} + \frac{1}{s}) = \frac{d}{2}(\frac{1}{30})\)
\(\frac{1}{s} = \frac{1}{30} - \frac{1}{90} = \frac{60}{2700} = \frac{2}{90}\)
\(s = \frac{90}{2} = 45.\) Ans - B.
15 Jul 2017, 21:07
Kudos
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aiming4mba
Three answers can be eliminated immediately: C, D, and E.
Distances are equal.
Overall average is 60.
One leg's speed is 90.
If one leg has speed 90, and overall average speed is 60,
the other leg is slower than 60 mph.
Eliminate answers C, D, and E
Answer A is out, too.
60 mph is 30 away from both 30 and 90 -- but we cannot average the averages.
Slower speeds take more, not equal, time.
By POE, Answer B
Check B) 45 mph
Assume D = 180
Leg 1 time = \(\frac{D}{r}=\frac{90mi}{90mph}=1\) hour
Leg 2 time = \(\frac{90mi}{45mph}=2\) hours
Ave speed \(=\frac{TotalD}{TotalT}=\frac{180}{3}=60\) mph
That's a match
Answer B
01 Jun 2018, 11:00
Kudos
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aiming4mba
There's a bit of ambiguity here.
If the first half of the trip is spent at one speed, and the second half is spent at another speed, are we referring to half the total DISTANCE, or half the total TIME.
For example, if it takes 10 hours to drive 200 miles, some people might refer to the first half of the trip as being the first 5 hours of driving. Others might refer to the first half of the trip as being the first 100 miles traveled.
That said, the official answer informs us that we're talking about half the DISTANCE.
To make things easier for us, let's assign a NICE VALUE to the TOTAL distance. That is, a number that works well with 60 and 90
Let's say the TOTAL distance is 540 miles.
This means the car traveled 270 miles at 90 mph, and the car traveled 270 miles at x mph.
It also means the car traveled the TOTAL 540 miles at an average speed of 60 mph
Let's start with a word equation: time spent driving 90 mph + time spent driving x mph = TOTAL time of trip
Time = distance/speed
So, we now get: 270/90 + 270/x = 540/60
Simplify to get: 3 + 270/x = 9
This means that 270/x = 6
Multiply both sides by x to get: 270 = 6x
Solve: x = 45 (mph)
Answer: B
Cheers,
Brent
