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taking turns driving

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by sanju09 » Fri May 07, 2010 5:07 am
Ally, Betty and Cathy are taking turns driving in a car from town A to town B, which is 100 miles apart. They all drive at constant rates. Ally covers a certain distance in half the time Cathy does, and Cathy can cover the same distance in twice the time Betty does. If Cathy drives for 20 miles and the total time taken for the journey is 2 hours, what is Ally's speed?
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
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by liferocks » Fri May 07, 2010 6:16 am
if distance is same time is inversely proportional to speed

so speed of A:speed of C=2:1
speed of B:speed of C=2:1
speed of A:speed of C:speed of B=2:1:2

so time taken for C to drive 20 miles=time taken for A to drive 40 miles =time taken for C to drive 40 miles

total time is 2*60 min or 120 min
20+40+40=100 miles every one has driven for same time=120/3=40min

speed of A=40/40*60 miles/hr=60miles/hr

Ans option C
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by analyst218 » Fri May 07, 2010 10:05 am
sanju09 wrote:Ally, Betty and Cathy are taking turns driving in a car from town A to town B, which is 100 miles apart. They all drive at constant rates. Ally covers a certain distance in half the time Cathy does, and Cathy can cover the same distance in twice the time Betty does. If Cathy drives for 20 miles and the total time taken for the journey is 2 hours, what is Ally's speed?
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
you can infer from the passage that Ally and Betty both travel twice the distance in equal length of time.
to make time equal you divided 2 hrs into 3 , which makes time 2/3 hrs for everyone.
since Ally travels twice 2x20=40 in 2/3 hrs, Ally's speed = 60
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