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Cars A and B are traveling from Town X to Town Y on the same

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Cars A and B are traveling from Town X to Town Y on the same

by Mike@Magoosh » Fri Jan 09, 2015 2:43 pm
Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A's speed is 1.25 times Car B's speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?
(A) 60 mph
(B) 75 mph
(C) 80 mph
(D) 96 mph
(E) 100 mph

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by fulltapori » Sat Jan 10, 2015 12:51 am
L----------------M---------------N

L point of overtake.
M point where B is when A reaches N ( town ).

LM = y miles ; MN = 35 miles
Speed of B = X mph
Speed of A = 1.25 X mph

Speed = dist/time =>

For A 1.25X = 35+y divide by 7/4 hrs
For B X = y divided by 7/4 hrs

from 1 & 2 we get :

y = 140 miles

putting this in speed equation for A gives 100 miles/hr.

Answer E
[spoiler][/spoiler]

---- Sorry i mistook the speed of A to be 1.5 times of B's speed instead of 1.25 times. I corrected the calculations ------
Last edited by fulltapori on Sat Jan 10, 2015 4:48 am, edited 4 times in total.
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by GMATGuruNY » Sat Jan 10, 2015 4:36 am
Since A catches up to B at 1:30pm, they are at the same location at this time.
By 3:15 pm -- 7/4 hours later -- B is behind A by 35 miles, implying that A travels 35 more miles than B in 7/4 hours.
Since A travels 35 more miles than B in 7/4 hours, the DIFFERENCE between A's rate and B's rate = 35/(7/4) = 20 miles per hour.

Since A's rate is 5/4 B's rate, for every 4 miles traveled by B, A travels 5 miles.
Thus, the rate ratio for A and B = 5:4 = 50:40 = 100:80, implying that A's rate = 100 miles per hour and B's rate = 80 miles per hour, for a rate difference of 20 miles per hour.

The correct answer is E.
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