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Two cars are traveling on a highway in the same direction. If car A

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Two cars are traveling on a highway in the same direction. If car A  [#permalink]

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New post Updated on: 07 Sep 2018, 18:17
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Question Stats:

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Two cars are traveling on a highway in the same direction. If car A traveling at a rate of 55 mph is 18 miles ahead of car B, which is traveling at 45 mph, how much time will it take for car A to double the distance between itself and car B?

A) 1 hour and 48 mins
B) 3 hours
C) 3 hours and 36 mins
D) 4 hours
E) 4 hours and 18 mins

Originally posted by jennysussna on 07 Sep 2018, 13:28.
Last edited by generis on 07 Sep 2018, 18:17, edited 1 time in total.
Edited and formatted the question, renamed the topic
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Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

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New post 07 Sep 2018, 15:24
jennysussna wrote:
Two cars are traveling on a highway in the same direction. if car A traveling at a rate of 55mph is 18 miles ahead of car B, which is traveling at 45 mph, how muh time will it take for car a to double the distance between itself and car b?

a 1 hour and 48 mins
b 3 hours
c 3 hours and 36 mins
d 4 hours
e 4 hours and 18 mins


This problem is almost equal to the one you have posted here:
https://gmatclub.com/forum/ps-same-dist ... l#p2127282

That´s why I will allow myself to answer this one more briefly (as I would do in the real test):

(See figure attached.)

B is virtually not-moving,
A is virtually with 10mph and (FOCUS) must travel another 18 miles (therefore it will be 2*18 miles ahead of A)...

Remember: virtual time = real time (our FOCUS), hence:

\(? = 18\,\,{\text{miles}}\,\,\left( {\frac{{1\,\,{\text{h}}}}{{10\,\,{\text{miles}}}}} \right)\,\,\, = \,\,\frac{{5 + 4}}{5}\,\,{\text{h}}\,\,{\text{ = }}\,\,1{\text{h}}\,\,{\text{ + }}\,\,\frac{4}{5}{\text{h}}\,\,\left( {\frac{{60\,\,\min }}{{1\,\,\,{\text{h}}}}} \right) = 1{\text{h}}48\min\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Two cars are traveling on a highway in the same direction. If car A  [#permalink]

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New post 07 Sep 2018, 17:38
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jennysussna wrote:
Two cars are traveling on a highway in the same direction. if car A traveling at a rate of 55mph is 18 miles ahead of car B, which is traveling at 45 mph, how muh time will it take for car a to double the distance between itself and car b?

a 1 hour and 48 mins
b 3 hours
c 3 hours and 36 mins
d 4 hours
e 4 hours and 18 mins

This is a "runaway" problem with a "gap" and a trap (gap distance that Car A must travel is not 36 miles).

Use RT=D and "solve for the gap."
We need
1) the rate at which the gap widens ("relative speed")
2) gap distance

(1) Rate = relative speed. Travel is in SAME direction. Subtract slower speed from faster. Relative speed: \((Rate_{A}-Rate_{B})=(55-45)=10mph\)

(2) Gap distance?
The gap distance at start: 18 miles
Desired gap distance? (18*2) = 36 miles
Car A is faster than B. The 18-mile distance between them never shrinks. It increases slowly.

Car A needs to get (36-18) = 18 ADDITIONAL miles ahead of Car B
\(D_{gap}=18\) miles

(3) TIME required?
How long for Car A to put another 18 miles between A and B?

Relative speed, \(R=10\) mph
Distance of gap, \(D=18\) miles
Time needed: \(RT=D\), so \(T=\frac{D}{R}\)
\(T=\frac{18}{10}=\frac{9}{5}=1\frac{4}{5}\) hours

Multiply any fraction of an hour by 60 to get minutes: \((\frac{4}{5}*60)=48\) minutes

Time needed: 1 hour, 48 minutes

ANSWER A



Check. From the time that A was 18 miles ahead of B to the time that A was 36 miles ahead of B, both cars traveled for \(\frac{9}{5}\) hours.

Start: Car B was at the 0 mile mark
RT=D, so Car B traveled \(45*\frac{9}{5}=81\) miles
End: Car B is at the 81-mile mark

Start: Car A started at the 18-mile mark
Car A traveled \(55*\frac{9}{5}=99\) miles
End: Car A is at mile marker (18+99) = 117

Distance between A and B? (117-81)=36 mi

That works.
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Two cars are traveling on a highway in the same direction. If car A &nbs [#permalink] 07 Sep 2018, 17:38
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