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# A car and a bicycle traveled in the same direction along the equal rou

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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Updated on: 08 Nov 2018, 02:04
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Difficulty:

35% (medium)

Question Stats:

81% (02:05) correct 19% (03:16) wrong based on 102 sessions

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[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 07 Nov 2018, 01:47. Last edited by MathRevolution on 08 Nov 2018, 02:04, edited 1 time in total. VP Joined: 09 Mar 2016 Posts: 1229 Re: A car and a bicycle traveled in the same direction along the equal rou [#permalink] ### Show Tags Updated on: 08 Nov 2018, 00:27 1 MathRevolution wrote: [Math Revolution GMAT math practice question] A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point? A. 15 min B. 20 min C. 25 min D. 30 min E. 35 min hey pushpitkc where am i wrong ? Why C is correct answer ? i am getting B if after 15 minutes the car passed a bike, it means that car covered 1/4 * 60 = 10 miles after overtaking bike so distance between car and bike is 10 miles so for bike to reach a waiting point is 1/3*60 = 20 minutes Bunuel maybe you can explain ? or you GMATGuruNY how about you ? Salsanousi Originally posted by dave13 on 07 Nov 2018, 09:34. Last edited by dave13 on 08 Nov 2018, 00:27, edited 2 times in total. VP Joined: 09 Mar 2016 Posts: 1229 Re: A car and a bicycle traveled in the same direction along the equal rou [#permalink] ### Show Tags 07 Nov 2018, 13:55 MathRevolution wrote: [Math Revolution GMAT math practice question] A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point? A. 15 min B. 20 min C. 25 min D. 30 min E. 35 min MathRevolution are you sure the OA is C ? I am getting B for some reason if C is the answer please provide your revolutionary explanation, just dont make it too complicated to understand Intern Joined: 23 Jun 2015 Posts: 26 Re: A car and a bicycle traveled in the same direction along the equal rou [#permalink] ### Show Tags 08 Nov 2018, 01:21 1 MathRevolution wrote: [Math Revolution GMAT math practice question] A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point? A. 15 min B. 20 min C. 25 min D. 30 min E. 35 min Dear all .. This question makes no sense to me . There is no clarity in the question . First of all , the starting point is not given . And then even if we consider the car crossed bicycle and travelled some 15 mins , the relative gap will be only 2.5 miles as both are travelling . There is no answer choice for this . So I don't think this question is a good question . Please let me know for any concerns . Thank you !! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8141 GMAT 1: 760 Q51 V42 GPA: 3.82 A car and a bicycle traveled in the same direction along the equal rou [#permalink] ### Show Tags 08 Nov 2018, 02:07 1 dave13 wrote: MathRevolution wrote: [Math Revolution GMAT math practice question] A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point? A. 15 min B. 20 min C. 25 min D. 30 min E. 35 min MathRevolution are you sure the OA is C ? I am getting B for some reason if C is the answer please provide your revolutionary explanation, just dont make it too complicated to understand Accidentally, the wrong answer is set. It is fixed now. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:18
1

But I don't know about this question and the way it is worded. I also doubt the answer choices, but it could just be me.

The way I approached it is that for the car it takes 15 minutes to travel 10 miles while the bicycle will cover 10 miles in 20 minutes.

So for the bicycle the distance covered is 30 * 1/4 = 7.5 miles.

Now it means that the car passed the bicycle by 2.5 miles. If we assume the car stopped there.

So it means the bicycle's time to reach the car is = distance/speed * 60 (to convert to minutes) = 2.5/30 * 60 = 5 minutes.

I hope someone else can validate this though. Perhaps chetan2u or Gladiator59

Thanks :D
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:36
1
1
Hello dave13

You are absolutely correct here and the original poster has updated the OA to correctly reflect B.

The way I tackled this question is - the relative speed of the car w.r.t the bicycle is 10 mph ( as 40 mph - 30 mph) in the same direction. So in 15 mins, the car will have travelled a distance of 10mph * ( 15/60) hr = 10/4 = 2.5 miles ahead of the bicycle.

Now, the bicycle traveling at 30 mph will take ( 2.5 miles / 30 mph) hrs or (2.5/30)*60 mins = 5 mins to reach that point where the car has halted.

Hence the bicycle travels for a total of 15 mins ( original when both car and bicycle are traveling) + 5 mins to catch up = 20 mins.

Hope this resolves your query! Let me know if you want to discuss some more.

Best,

dave13 wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

hey pushpitkc where am i wrong ?

Why C is correct answer ? i am getting B

if after 15 minutes the car passed a bike, it means that car covered 1/4 * 60 = 10 miles after overtaking bike

so distance between car and bike is 10 miles

so for bike to reach a waiting point is 1/3*60 = 20 minutes

Bunuel maybe you can explain ? or you GMATGuruNY

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Regards,

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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:38
1
Hi Salsanousi,

Your approach is correct. So the bicycle does take 5 mins to catch up to the car. However, the bicycle has already travelled for 15 mins and hence the total travel time is 20 mins.

Hope this resolves the confusion. Let me know if you want to discuss further.

Best,

Salsanousi wrote:

But I don't know about this question and the way it is worded. I also doubt the answer choices, but it could just be me.

The way I approached it is that for the car it takes 15 minutes to travel 10 miles while the bicycle will cover 10 miles in 20 minutes.

So for the bicycle the distance covered is 30 * 1/4 = 7.5 miles.

Now it means that the car passed the bicycle by 2.5 miles. If we assume the car stopped there.

So it means the bicycle's time to reach the car is = distance/speed * 60 (to convert to minutes) = 2.5/30 * 60 = 5 minutes.

I hope someone else can validate this though. Perhaps chetan2u or Gladiator59

Thanks :D

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
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Joined: 19 Oct 2013
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:43
1
1

The wording "how long it takes the bicycle to reach the waiting point?" doesn't that mean 5 minutes?

It doesn't ask for the total period travelled? I'm not sure though about the wording as it confused me.

Thanks!
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:47
I would agree with you, the question could have been better worded. However, on looking at the options it becomes clear that the question intends to ask the total time.

Best,

Salsanousi wrote:

The wording "how long it takes the bicycle to reach the waiting point?" doesn't that mean 5 minutes?

It doesn't ask for the total period travelled? I'm not sure though about the wording as it confused me.

Thanks!

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Regards,

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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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08 Nov 2018, 03:56
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

It is given that the car reaches the waiting point 15 minutes after crossing the bi-cycle,
so distance traveled by car in 15 min = 40*(15/60) = 10 miles

so, time taken by bi-cycle to travel 10 miles = 20 minutes. (bcz, speed of bicycle is given 30 miles in an hour, which means it covers 10 miles every 1/3 hrs which is nothing but 20 minutes).

so, option B is correct.
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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09 Nov 2018, 01:24
=>

Since the car traveled for $$15$$ minutes with the speed $$40$$ mph, it moved $$10$$ miles. It take $$20$$ minutes the bicycle to travel $$10$$ miles with the speed $$30$$ mph.

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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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09 Nov 2018, 01:47
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

The wording of the question is too bad.
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Re: A car and a bicycle traveled in the same direction along the equal rou  [#permalink]

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09 Nov 2018, 13:18
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

In 15 minutes, or 1/4 of an hour, the car travels 40/4 miles and the bicycle travels 30/4 miles.

Thus, the bicycle needs to travel 40/4 - 30/4 = 10/4 = 5/2 miles to reach the car.

The bicycle will travel 5/2 miles in (5/2)/30 = 5/60 = 1/12 hour, which is 60 x 1/12 = 5 minutes.

Including the 15 minutes that the bike has already traveled, it takes 15 + 5 = 20 minutes for the bike to reach the waiting point.

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Re: A car and a bicycle traveled in the same direction along the equal rou   [#permalink] 09 Nov 2018, 13:18
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