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susheelh
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 19 Aug 2016, 22:34
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E
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85% (hard)

Question Stats:

57% (02:59) correct 43% (03:17) wrong based on 217 sessions

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Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40
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E
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- Updated on: 28 Nov 2016, 09:17
Originally posted by abhimahna on 20 Aug 2016, 01:36.
Last edited by abhimahna on 28 Nov 2016, 09:17, edited 1 time in total.
Corrected a Typo
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susheelh
Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40
Show more

Original Equations : T1 = D /S

When 3mph faster, T2 = D/S+3

When 2mph Slower, T3 = D/S-2

Now, as per questions we are given T1-T2 = 40 mins or 2/3 hours

or D/S - D/S+3 = 2/3

or D = 2S(S+3)/9 --- (1)

Also, T3-T1 = 2/3 hours

or D = S(S-2)/3 --- (2)

Equating (1) and (2), We will have S = 12 mph

or put the value of S in (1), we will get D = 40 miles. Hence, E
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 01 Nov 2016, 19:02
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Is there a more elegant method to solve these questions. The calculations kind of become long winded and prone to misclaculations.

Thanks
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 01 Nov 2016, 23:26
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susheelh
Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40
Show more

(s + 3)*(t - 2/3) = st = Certain Distance
3t - (2/3)s = 2 .........(I)

(s - 2)*(t + 2/3) = st = Certain Distance
(2/3)s -2t = 4/3 .........(II)

Add (I) and (II) to get
t = 10/3
s = 12
Distance = 12*10/3 = 40 miles
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 28 Nov 2016, 08:26
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abhimahna
susheelh
Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40

Original Equations : T1 = D /S

When 3mph faster, T2 = D/S+3

When 2mph Slower, T3 = D/S-2

Now, as per questions we are given T1-T2 = 40 mins or 2/3 hours

or D/S - D/S+3 = 2/3

or D = 2S(S+3)/9 --- (1)

Also, T1-T3 = 2/3 hours

or D = S(S-2)/3 --- (2)

Equating (1) and (2), We will have S = 12 mph

or put the value of S in (1), we will get D = 40 miles. Hence, E
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hi abhimahna

seems something wrong with the above equations...
Please correct me if my understanding is wrong...

thanks
rohit
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 28 Nov 2016, 09:10
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rohit8865
abhimahna
susheelh
Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40

Original Equations : T1 = D /S

When 3mph faster, T2 = D/S+3

When 2mph Slower, T3 = D/S-2

Now, as per questions we are given T1-T2 = 40 mins or 2/3 hours

or D/S - D/S+3 = 2/3

or D = 2S(S+3)/9 --- (1)

Also, T1-T3 = 2/3 hours

or D = S(S-2)/3 --- (2)

Equating (1) and (2), We will have S = 12 mph

or put the value of S in (1), we will get D = 40 miles. Hence, E

hi abhimahna

seems something wrong with the above equations...
Please correct me if my understanding is wrong...

thanks
rohit
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T1, T2 and T3 are the times, I mentioned.

Note that when someone is faster, time taken is less and when someone is slower time taken is more.

So, as per the question stem, I believe 1st statement is correct and I wrote the 2nd equation in reverse order. It is a typo. Edited the original solution.

Please let me know if you find any other flaw.
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 23 Jun 2019, 11:33
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susheelh
Anthony covers a certain distance on a bike. Had he moved 3mph faster, he would have taken 40 Minutes less. Had he moved 2mph slower, he would have taken 40 minutes more. The distance (in miles) is -

A. 30
B. 35
C. 36
D. 37.5
E. 40
Show more

We can let the distance = d and his rate = r. Thus, we can create the equations (notice that 40 minutes = 2/3 hour):

d/(r + 3) = d/r - 2/3

and

d/(r - 2) = d/r + 2/3

Subtracting the first equation from the second, we have:

d/(r - 2) - d/(r + 3) = 4/3

Multiplying by 3(r - 2)(r + 3), we have:

3d(r + 3) - 3d(r - 2) = 4(r - 2)(r + 3)

3dr + 9d - 3dr + 6d = 4(r - 2)(r + 3)

15d = 4(r - 2)(r + 3)

d = 4(r - 2)(r + 3)/15

Substituting this back into the first equation, we have:

[4(r - 2)(r + 3)/15](r + 3) = [4(r - 2)(r + 3)/15]/r - 2/3

4(r - 2)/15 = 4(r - 2)(r + 3)/(15r) - 2/3

Multiplying by 15r, we have:

4r(r - 2) = 4(r - 2)(r + 3) - 10r

4r^2 - 8r = 4(r^2 + r - 6) - 10r

4r^2 - 8r = 4r^2 + 4r - 24 - 10r

-8r = -6r - 24

-2r = -24

r = 12

So d = 4(12 - 2)(12 + 3)/15= 4(10)(15)/15 = 40 miles.

Answer: E
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Anthony covers a certain distance on a bike. Had he moved 3mph faster- 18 Dec 2024, 01:14
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