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how do i solve this

by grandh01 » Thu Aug 02, 2012 8:52 pm
20. How many miles long is the route
from Houghton to Callahan?

(1) It will take 1 hour less time to
travel the entire route at an
average rate of 55 miles per hour
than at an average rate of 50
miles per hour.
(2) It will take 11 hours to travel the
first half of the route at an
average rate of 25 miles per hour.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Aug 02, 2012 9:23 pm
grandh01 wrote:20. How many miles long is the route
from Houghton to Callahan?

(1) It will take 1 hour less time to
travel the entire route at an
average rate of 55 miles per hour
than at an average rate of 50
miles per hour.
(2) It will take 11 hours to travel the
first half of the route at an
average rate of 25 miles per hour.
(1) If the time taken to travel the entire distance is t, then distance = (t - 1) * 55 = t * 50
Solving the above equation, we get, 55t - 55 = 50t
5t = 55
t = 11
So, distance = 11 * 50 = 550 miles; SUFFICIENT.

(2) If the total distance = d, then d/2 = 11 * 25
d = 2 * 11 * 25 = 550 miles; SUFFICIENT.

The correct answer is D.
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by [email protected] » Fri Aug 03, 2012 7:36 pm
Hi grandh01,

Always try to prepare equations when you are
given problems with some non numerical values.

In this question you are told that the time to cover
a distance covered at 55 mph is 1 hour less than the time
to cover the same distance in 50mph.

I>
So you need to consider the time as 't' because
speed*time=distance, (We know speed but not time, and distance being equal we equate)
Now,

50*t=55(t-1) (Since at 55mph he would have covered the same distance in 1 less than t hours)
If we equate we get the value.
Hence it is sufficient.

II>
Half distance in 11 hours at 25 mph.
So distance is
25*11=275miles
hence if half is known we can calculate full.

Answer : D

Small tip : Never sit down and calculate if you know the answer is achievable. Its simply
a waste of time.
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