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Jane covered a distance

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Jane covered a distance

by sanju09 » Tue Apr 05, 2011 4:49 am
Jane covered a distance of 340 miles between two cities taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour speed?
(A) 1 ½ hours
(B) 1 ¾ hours
(C) 2 hours
(D) 2 ½ hours
(E) 3 hours
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by rohu27 » Tue Apr 05, 2011 4:56 am
340=(60*t1)+(80*(5-t1))
total distance=sum of the individual distances
on solving,
20t1=60,t1=3
option E
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by Anurag@Gurome » Tue Apr 05, 2011 5:00 am
sanju09 wrote:Jane covered a distance of 340 miles between two cities taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour speed?
(A) 1 ½ hours
(B) 1 ¾ hours
(C) 2 hours
(D) 2 ½ hours
(E) 3 hours
Distance(D) = 340 miles, Time(T) = 5 hours, Speed = D/T = 340/5 = 68 mph
Let the distance covered at 60 mph = x miles; Time = x/60 hours
Then distance covered are 80 mph = (340 - x) miles; Time = (340 - x)/80 hours
So, x/60 + (340 - x)/80 = 5 or 20x + 20400 = 24000
Solving , we get x = 180, which implies at 60 mph Jane traveled for 180/60 = 3 hours

The correct answer is E.
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by GMATGuruNY » Tue Apr 05, 2011 5:12 am
sanju09 wrote:Jane covered a distance of 340 miles between two cities taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour speed?
(A) 1 ½ hours
(B) 1 ¾ hours
(C) 2 hours
(D) 2 ½ hours
(E) 3 hours
Very little math is needed here.

If Jane had spent an equal amount of time (5/2 = 2.5 hours) travelling at each speed (60 and 80), the average rate for the whole trip would be (60+80)/2 = 70 miles per hour.
Average speed for the whole trip = d/t = 340/5 = 68 miles per hour.
68 is closer to 60 than to 80.
Thus, more than half the time -- in other words, more than 2.5 hours -- was spent travelling at 60 miles per hour.

The correct answer is E.
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