A car starts 2/5 of a mile behind a bus that is traveling at : Problem Solving (PS)

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

02 Nov 2012, 09:53

Bunuel wrote:

roygush wrote:

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

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.

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?

L

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

02 Nov 2012, 09:57

Expert Reply

roygush wrote:

Bunuel wrote:

roygush wrote:

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

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.

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?

Check for theory here: gmat-math-book-87417.html

For practice: viewforumtags.php

Hope it helps.

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

02 Nov 2012, 13:19

MacFauz wrote:

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 * 2/30 = 2.4

Answer is B.

Kudos Please... If my post helped.

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?

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

02 Nov 2012, 21:31

actleader wrote:

MacFauz wrote:

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 * 2/30 = 2.4

Answer is B.

Kudos Please... If my post helped.

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?

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.

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

03 Nov 2012, 07:37

MacFauz wrote:

actleader wrote:

MacFauz wrote:

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 * 2/30 = 2.4

Answer is B.

Kudos Please... If my post helped.

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.

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

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

04 Nov 2012, 05:14

1

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

s=72 m/h

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

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Re: A car starts 2/5 of a mile behind a bus [#permalink]

14 Nov 2012, 03:50

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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.

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

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

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

28 Sep 2013, 02:51

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 [Since it is relative speed => x-60]

x=72 miles/hour

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

Hence (B)

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

21 Oct 2013, 10:48

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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

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

21 Nov 2013, 11:20

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

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A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

14 May 2018, 19:29

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Expert Reply

roygush wrote:

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

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

B

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

14 May 2018, 21:53

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.

P

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

15 May 2018, 16:08

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roygush wrote:

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

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

B

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

03 Oct 2018, 00:59

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)

S

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

07 Apr 2021, 05:01

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)

B

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

28 Apr 2022, 10:29

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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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

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Re: A car starts 2/5 of a mile behind a bus that is traveling at [#permalink]

27 Mar 2024, 06:20

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