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

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Intern
Joined: 24 May 2018
Posts: 6
Two cars are traveling on a highway in the same direction. If car A  [#permalink]

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Updated on: 07 Sep 2018, 17:17
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:46) correct 45% (02:08) wrong based on 39 sessions

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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, 12:28.
Last edited by generis on 07 Sep 2018, 17:17, edited 1 time in total.
Edited and formatted the question, renamed the topic
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 730
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

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07 Sep 2018, 14:24
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.
Attachments

07Set18_9y.gif [ 3.55 KiB | Viewed 590 times ]

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

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07 Sep 2018, 16:38
1
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

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   [#permalink] 07 Sep 2018, 16:38
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