A car starts 2/5 of a mile behind a bus that is traveling at

Question

A car starts 2/5 of a mile behind a bus that is traveling at 60 miles per hour. If the car catches up to the bus after 2 minutes, how many miles does the car travel in that time?

A.  2\frac{1}{10}

B.  2\frac{2}{5}

C.  2\frac{1}{2}

D.  2\frac{7}{8}

E. 3

I am not sure how to approach this one.
my intuition says either B or C. 
please help.
thank you

Bunuel · Accepted Answer

Car traveled the distance that the bus covered in 1/30 hours (2 minutes) plus 2/5 miles, thus 60*\frac{1}{30}+\frac{2}{5}=2\frac{2}{5} miles. Answer: B. Hope it's clear. P.S. Please indicate OA for PS problems (rule #7 here: rules-for-posting-please-read-this-before-posting-133935.html). Thank you.

MacFauz · Answer

My method was :

Car is travelling at a speed of 2/5 miles per 2 mins faster than the bus
i.e 12 mph faster than the buse
= 72 mph

So in 2 mins = 72 * 2/60 = 2.4

Answer is B.

Kudos Please... If my post helped.

roygush · Answer

Kudos and thank you both for your help, it is clear.
i knew it was easy...
Bunuel, ive been going through your posts. can you please create a post with Word Problems? like tips and tricks for Work/Rate/Ratio/Precents?

Bunuel · Answer

Check for theory here: gmat-math-book-87417.html For practice: viewforumtags.php Hope it helps.

actleader · Answer

Please explain your calculations...to say it rightly - formula

where did you get 12 mph and 72 mph and why did you divide it into 2/30?

MacFauz · Answer

Thanks for pointing it out. It was a typo.. Was thinkin 2/60(Conversion from minutes to hours since speed is in mph) equals 1/30 and typed in 2/30. I've changed that now. As for the remaining calculations. The car catches up the distance of 2/5 of a mile with the bus in 2 minutes. So the car must be travelling at a speed of 2/5 miles per 2 mins faster than the bus. 2/5 miles per 2 minutes is (2/5)*(60/2) mph. = 12 mph. Since this is the speed that the car is travelling at in excess to the speed of the bus, to get the speed of the car, we have to add this to the speed of the bus. 60 + 12 = 72

Kudos Please... If my post helped.

actleader · Answer

Now I see what  (2/5)*(60/2) mph. = 12 mph  means and where you got it.
It is a   /   that represented the increasing in speed.

LalaB · Answer

(S-60)*(2/60)=2/5

s=72 m/h

72*(2/60)=2 2/5 miles

mbaiseasy · Answer

In order for a car to catch up to the bus, it must travel the gap plus the additional distance travelled by the bus in two minutes.

\frac{60miles}{hour}x\frac{1 hour}{60minutes}x 2minutes=2miles

d=gap + d of bus 
 d=\frac{2}{5}miles + 2 miles = 2\frac{2}{5}miles

TGC · Answer

Let 'x' be the speed of the CAR in miles/hour

Distance covered in catching the bus/ Relative speed of the car = Time taken (2 min)

2/(5* (x-60) = 2/60

x=72 miles/hour

Distance traveled by car = Speed(x) * time(2 min)

Hence (B)

Spunkerspawn · Answer

The bus travels at 60mph = 1 mile per minute so in 2 minutes the bus has traveled 2 miles. If the car has caught up with the bus in 2 minutes, then it has driven 2 2/5 miles since it started 2/5 miles behind the bus.

Answer: B

Answer: B

AccipiterQ · Answer

I looked at it as a relative speed problem; both going 60 mph the car would never catch up. But in 2 minutes it traveled an extra 2/5 of a mile, so the speed it used to cover that extra 2/5 would be 30(since 30*2=60)*2/5=60/5=12mph extra, add that to the 60mph of the bus and you get 72 mph, divide by 1/30 of an hour, and you get 2.4

generis · Answer

Gap closes at what speed? 
Find the "relative speed" at which the gap closes
Divide gap distance by time
Distance =  \frac{2}{5}  mile
Time = 2 minutes =  \frac{1}{30}  hour 
 
Rate (speed) at which gap closes,:  r=\frac{D}{t} 
Relative speed:
 r=\frac{(\frac{2}{5})}{(\frac{1}{30})}=(\frac{2}{5}*\frac{30}{1})=12  mph

In this "chase," the gap closes at a relative speed of 12 mph

Car's rate? 
(Car rate - bus rate) = relative speed
(Car rate - 60 mph) = 12 mph
Car rate = 72 mph

Distance the car travels in 2 minutes? 
Time: 2 minutes =  \frac{1}{30}  hour
Rate: 72 mph 
Distance traveled: 
  r*t=D :
 (72*\frac{1}{30})=\frac{72}{30}=\frac{12}{5}=2\frac{2}{5}   miles

Answer B

el2010 · Answer

Bus travels 60mph so the bus travels 1mi per minute. Assume bus starts at mile #1 and the car is 2/5 mi behind so 1-(2/5) - 3/5mi (starting point). In 2 minutes, the bus traveled 2mi from mile #1 to mile #3. To calculate the time for the car to catch up to the bus (which is at mile #3), 3-(3/5) = 12/5 minutes. Answer Choice B.

JeffTargetTestPrep · Answer

In the 2-minute time period, we note that both the car and the bus have traveled for 2/60 of an hour. We can let r = the rate of the car and create the equation:

r(2/60) = 60(2/60) + 2/5

r/30 = 2 + 2/5

Multiplying by 30, we have:

r = 60 + 12

r = 72

So in 2 minutes the car traveled 72 x 2/60 = 72/30 = 12/5 = 2 2/5 miles.

Answer: B

jalice · Answer

Travelling rate of bus=60/60= 1 mile/min
So, in 2 min it will travel=2 miles

As car has to catch bus, it has to travel= 2+(2/5)= 12/5 miles

(B)

Abhibarua · Answer

Catching up means the car traveled the distance that it was behind the bus (2/5 miles) as well as the distance the bus has traveled until both the vehicles are in the same position.

If the bus travels 60 miles in 60 minutes (or 1 hour), it will travel 2 miles in 2 minutes.

So the car traveled 2/5 + 2 miles. (Option: B)

priyankagh · Answer

So this is how I solved the question: 
First, I calculated how much the bus traveled in 2 mins, which is 2 miles. Since it is a "catching up" type of question, the car must've also traveled those 2 miles to catch up with the bus. Additionally, it traveled 2/5th of a mile so the total distance traveled by car comes to 2+2/5. 
Is there any logical flaw in my solution?  Bunuel   JeffTargetTestPrep

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A car starts 2/5 of a mile behind a bus that is traveling at

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