RTD

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RTD

by J N » Sun May 26, 2013 3:41 pm
if a motorist had driven 1 hour longer and at average rate of 5 miles per hour faster, he would have covered 70 more miles. how many more miles would he have covered if he had driven 2 hours longer and at average rate of 10 miles per hour faster




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answer 150

RT +70 = (R+5)(T+1).....got messy must be better way
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by ygdrasil24 » Sun May 26, 2013 10:52 pm
So he travelled 70 miles in 1 hour, so speed had been 70 miles/hr. But this speed was 5 miles more than actual, so actual speed was 65.
So in 2 hrs and travelling at a speed of 65+10, he would have covered, 2 * 75 = 150 miles.

Second Approach:

In 1 hr - travelling 5miles/hr faster - covers 70 miles
So in 2 hr - travelling 5 miles/hr faster - covers - 140 miles.
So in 2 hr - travelling 5 + 5 miles/hr - covers - 140 + (2*5) = 150 miles.
This way one need not calculate the original speed.

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by aaggar7 » Mon May 27, 2013 1:59 am
Initial condition :

RT = D --(1)

According to 1st condition

(R + 5) (T + 1) = D + 70 -- (2)

From 1 D = RT

SO 2 becomes

(R + 5) (T + 1) = RT +70

=> RT + R + 5T + 5 = RT + 70

=> R + 5T = 65 -- (3)

3re condition,

(R + 10) (T + 2 ) = Let X

RT + 2R + 10 T + 20 =X

RT +2 (R + 5T) + 20 = X -- (4)

From 3,R + 5 T = 65

So,4 becomes

RT + 2 *65 + 20 =X

As RT= D
==> D + 150 = X

Hence,answer is 150 :).

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by GMATGuruNY » Mon May 27, 2013 2:55 am
J N wrote:If a motorist had driven 1 hour longer and at average rate of 5 miles per hour faster, he would have covered 70 more miles. How many more miles would he have covered if he had driven 2 hours longer and at average rate of 10 miles per hour faster?

100
120
140
150
160
The distance traveled in the extra hour = 70 miles.
The 70 miles traveled in this hour = 5 miles per hour FASTER than the actual rate.
Thus, the actual rate = 70-5 = 65 miles per hour.
10 miles per hour faster = 65+10 = 75 miles per hour.
Distance traveled in 2 hours at 75 miles per hour = 2*75 = 150.

The correct answer is D.
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by Atekihcan » Tue May 28, 2013 9:21 am
@ygdrasil24 : Both of them are brilliant solution. :)

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by ygdrasil24 » Mon Jun 03, 2013 12:57 am
Atekihcan Thanx Mate
Click on thanx button then :P