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

Question

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

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

generis · Accepted Answer

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 and ahead of car B. 
The 18-mile distance between them  never  shrinks. Rather, that gap 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 will it take 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.

fskilnik · Answer

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\,\,{ ext{miles}}\,\,\left( {\frac{{1\,\,{ ext{h}}}}{{10\,\,{ ext{miles}}}}} ight)\,\,\, = \,\,\frac{{5 + 4}}{5}\,\,{ ext{h}}\,\,{ ext{ = }}\,\,1{ ext{h}}\,\,{ ext{ + }}\,\,\frac{4}{5}{ ext{h}}\,\,\left( {\frac{{60\,\,\min }}{{1\,\,\,{ ext{h}}}}} ight) = 1{ ext{h}}48\min This solution follows the notations and rationale taught in the GMATH method. Regards, fskilnik.

dcwanderer30 · Answer

What's the source of this question?

effatara · Answer

Car A is 10 mph faster than Car B so it gains 10 miles in 1 hour on Car B. In order to double the distance the distance between them, Car A will have to gain 18 miles on Car B to do which it will need 18/10=1.8 hours=1 hr 48 mins. Ans: A.

kumarankit01 · Answer

here relative speed = 55-45 = 10 mph

current distance = 18 
target distance = 36
required extra distance=18

It means we have to calculate how much time it will take to cover 18 miles with relative speed of 10 mph

time = 18/10 = 1.8 hours

so 1 hour and 48 mins

Posted from my mobile device

ankitsood5 · Answer

Relative speed is 10 mph, to cover 18 miles it would take a bit less than 2 hours, Only option A is less than 2 hours, hence is the correct answer.
Nice to go through the options before going into the calculations.

Kinshook · Answer

Given: Two cars are traveling on a highway in the same direction.

Asked: 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?

Relative speed = 55 - 45 = 10 mph
Distance to be covered = 18 miles
Time required = 18/10 = 1.8 hours = 1 hour 48 mins

IMO A

ScottTargetTestPrep · Answer

Solution:

We see that car A needs to travel 18 more miles than car B to double the distance between itself and car B since it’s already 18 miles ahead of car B. If we let t be the number of hours it takes car A to do so, we can create the equation:

55t = 45t + 18

10t = 18

t = 1.8

We see that it takes car A 1.8 hours, or 1 hour and 48 minutes, to double the distance between itself and car B.

Answer: A

Paras96 · Answer

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

By the concept of relative speed, because both the cars are traveling in the same direction
=> relative speed, V = 55-45=10

Distance = 18

Time taken = Distance/Speed=18/10= 1.8 hours = 1 hours 48 minutes

Hence A

btsaami · Answer

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

-->  If starting together, A travels 55 miles in 1 hour and B travels 45 miles per hour, so in each hour A would have been 10 km ahead of B. Now, A is already 18 km ahead of B, we have to check when the distance between the two becomes 36km. In the next 1 hour, A will travel 10km ahead of B which results in net distance 18+10= 28km.

In next hour, 28+10= 38. Therefore, the time taken to double the distance (<2 hours) will be 1 hour 48 min.

bumpbot · Answer

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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

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