Two cars travel on a highway in the same direction. If car A travels

Question

Two cars travel on a highway in the same direction. If car A travels at a rate of 75 mph and is \(y\) miles ahead of car B, which is traveling at 60 mph, in terms of \(y\), how many miles must car A travel to double the distance between itself and car B?

A) 3y
B) 4y
C) 5y
D) 6y
E) 8y

A) 3y
B) 4y
C) 5y
D) 6y
E) 8y

Neferteena · Accepted Answer

This is an expanding gap problem.
gap -> distance between two cars A & B
gap = y miles( given)

Question - Time taken by A to double the gap between A & B.
Find time taken by the gap , t= distance/ relative speed

t= y/(75-60) = y/15

time taken to cover y miles of gap is y/15.

Car A is already y miles apart, to double the gap , Car A needs to travel y/15 more hours.

distance travelled by Car A in y/15 hours = 75 * y/15 = 5y.

Ans: 5y

fskilnik · Answer

This is an excellent opportunity to use "relative velocity" (in what we call the  chasing scenario ), carefully explained in our method!

The "starting point" is shown in the figure attached.

Let B stay still (virtual velocity zero) and A travel at a virtual speed of 15mph (75-60).

The temporary focus is (always!) the virtual time (equal to the real one!), in this case, time for A to travel y (extra) miles in its virtual speed....

To find that, let´s use the powerful UNITS CONTROL!

y\,\,{	ext{miles}}\,\,\left( {\frac{{1\,\,{	ext{h}}}}{{15\,\,{	ext{miles}}}}} ight)\,\,\, = \,\,\frac{y}{{15}}\,\,{	ext{h}}

Finally we go back to A´s real velocity/speed, using again UNITS CONTROL:

?\,\, = \,\,\,75\,\,\left( {\frac{{{	ext{miles}}}}{{	ext{h}}}} ight)\,\, \cdot \,\,\frac{y}{{15}}\,\,{	ext{h}}\,\,\,\,{	ext{ = }}\,\,\,{	ext{5y}}\,\,\,{	ext{miles}}

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

Regards,
fskilnik.

generis · Answer

This problem is a "runaway." Faster car A starts at a "gap" distance of  y  miles ahead of B. Car A pulls away from B and until the  y -mile gap between them doubles.

How far   A  must travel  (to double  y ) is the key and the trap.  y  doubled is not the issue. 2y is not the answer.

The issue: Car A has to double  y  miles  while B still moves  during Leg 2.

One method: Choose a time traveled for Leg 1 to "assign"  y

(1)  Original gap of  y  miles? 
• Assign a time based on relative speed
• SAME direction of travel? Subtract to get relative speed, 
  R=(Rate_{A}-Rate_{B})=(75-60)=15mph

• Let Leg 1 travel time = 2 hours
Car A traveled  (75*2) = 150  mi
Car B traveled  (60*2) =120  mi
Car A is  (150-120) = 30  miles ahead of B
Starting gap distance  y= 30 
 
 (2)  Distance that A must travel to double  y=30 ?
• start distance gap: 30 miles
• Desired distance gap: (30 * 2) = 60 miles
Car A travels (60-30) = 30  additional  miles
• Car A does NOT cover 60 more miles. The 30-mile original gap  never  shrinks. It increases slowly, by 30 miles, to 60 miles

(3)  Time for A to cover Leg 2 = 30 more miles? B still moves. 
Use relative speed, R = 15 mph. D = 30
RT = D, so   T=\frac{D}{R}  
A's time:  \frac{30mi}{15mph}=2  hrs

(4)  Distance that A traveled in Leg 2?
• (A's speed * A's time) = A's distance
• A's distance:  (75mph*2hrs)=150  miles
• A traveled 150 miles to double the original gap

(5)   150  miles in terms of  y=30 ?  \frac{150}{30}=5 
 150=5y

Answer C

satya2029 · Answer

(75-60)*t= Y
t=Y/15
Distance travelled by A in time t=75*Y/15
=5Y
C:)

bmsaqifansary · Answer

We know 3 facts.

A speed- 75 mph
B speed- 60 mph
Gap=Y

The trick is understanding the question is not asking us to find distance for distance traveled 2*Y but rather,
GAP+GAP=2*the gap. We already know the gap is "Y miles",we need to find distance A needs to travel to make another "Y miles" GAP.

So, the equation we can derive,

GAP=(Speed of A* Time)-(Speed of B*Time)

75T-60T=Y miles

T=Y/15 Miles
(Note: Time will be same for both the cars when they are "Y" miles apart)

Therefore,

Distance A Travels= (Time)*(Speed of A)

=75 mph * Y/15 = 5Y

This is a layman solution, you can solve this less than 2 mins as long as you get the trick.
Answer (C)

Kinshook · Answer

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

Asked: If car A travels at a rate of 75 mph and is  y  miles ahead of car B, which is traveling at 60 mph, in terms of  y , how many miles must car A travel to double the distance between itself and car B?

Relative speed = 75 - 60 = 15 mph
Relative Distance = y miles
TIme = y/15 hrs

Actual distance to be travelled = (y/15)*75 = 5y

IMO C

CAMANISHPARMAR · Answer

Simple answer:-

A is travelling at a higher speed than B, therefore, relative speed =  R=(Rate_{A}-Rate_{B})=(75-60)=15mph

The time A will take to double the distance is  \frac{y}{15}  hours

So the distance covered by A in  \frac{y}{15}  hours is  \,\,\,{	ext{5y}}\,\,\,{	ext{miles}}  (Answer)

gurmukh · Answer

Distance = 75×y/15
 =5y

Posted from my mobile device

st1gg3r · Answer

Car A's speed:75mph
Car B's speed:60mph

Ratio of speeds of Car A and Car B 5:4 = Ratio of their distances Distance A: Distance B = 5:4
Difference is 1. So when A travels 5 units B travels 4 unit.

Since current distance between them is y and we need to double it to 2y that means the gap between A and B has to increase by y more miles.

So when gap is 1 A trvels 5 unit distance and B travels 4 unit distance. 
When gap is y, A travels 5y unit distance and B travels 4y unit distance.

Answer is 5y. Option C.

Krishant92 · Answer

I solved it in the way below
Ratio of speeds is
75:60= 5:4 which means if A travels 5m, B travels 4 miles.
Difference is distance (y)= 1 mile
Q asked is double the distance (2y)= 2 miles = (A=10miles & B=8miles)
Total travelled by A to achieve 2y = 10-5=5

Is my approach correct?

Answer- C

bumpbot · Answer

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Two cars travel on a highway in the same direction. If car A travels

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