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A car travelling from city A to B takes an hour lesser to cover the di

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A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Nov 2019, 06:14
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A car travelling from city A to B takes an hour lesser to cover the distance if it moved 10 kilometres per hour faster. On the other hand it will take an hour more to cover the distance if it moved 6 kilometres per hour slower. What is the distance between the two cities?

A. 120 kilometres
B. 150 kilometres
C. 180 kilometres
D. 360 kilometres
E. 380 kilometres


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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Nov 2019, 06:40
2
Distance = Speed (s) x time (t)
Case 1: If speed is (s+10), then time taken is (t-1)
Case 2: If speed is (s-6), then time taken is (t+1)

From Case 1,
Distance = st = (s+10)*(t-1) = st - s + 10t -10 Or, s-10t+10 = 0
From Case 2,
Distance = st = (s-6)*(t+1) = st + s - 6t - 6 Or, s - 6t - 6 = 0

Solving the above two equations, we get t = 4 h
Plugging in value of t in the above equations gives s = 30 kmph

Therefore Distance = 30*4 = 120 km

Ans (A)
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A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Nov 2019, 07:05
navaneethmmb wrote:
Distance = Speed (s) x time (t)
Case 1: If speed is (s+10), then time taken is (t-1)
Case 2: If speed is (s-6), then time taken is (t+1)

From Case 1,
Distance = st = (s+10)*(t-1) = st - s + 10t -10 Or, s-10t+10 = 0
From Case 2,
Distance = st = (s-6)*(t+1) = st + s - 6t - 6 Or, s - 6t - 6 = 0

Solving the above two equations, we get t = 4 h
Plugging in value of t in the above equations gives s = 30 kmph

Therefore Distance = 30*4 = 120 km

Ans (A)


Can you kindly explain why you equated the two equations in case 1 and case 2 to 0?
Thanks
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Nov 2019, 08:37
Bunuel wrote:
A car travelling from city A to B takes an hour lesser to cover the distance if it moved 10 kilometres per hour faster. On the other hand it will take an hour more to cover the distance if it moved 6 kilometres per hour slower. What is the distance between the two cities?

A. 120 kilometres
B. 150 kilometres
C. 180 kilometres
D. 360 kilometres
E. 380 kilometres


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given
d=s*t
(t-1)*(s+10) = (t+1)*(s-6)
LHS = 10t-s=10
and RHS = s-6t=6
add both ; we get t= 4 hrs and s= 30 kmph
d= 120 km
IMO A
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 07 Nov 2019, 19:53
2
1
Bunuel wrote:
A car travelling from city A to B takes an hour lesser to cover the distance if it moved 10 kilometres per hour faster. On the other hand it will take an hour more to cover the distance if it moved 6 kilometres per hour slower. What is the distance between the two cities?

A. 120 kilometres
B. 150 kilometres
C. 180 kilometres
D. 360 kilometres
E. 380 kilometres


Are You Up For the Challenge: 700 Level Questions


We can create the equations:

rt = d (Eq. 1)

and

(r + 10)(t - 1) = d (Eq. 2)


and

(r - 6)(t + 1) = d (Eq. 3)

Equating the left hand sides of Eq. 1 and Eq. 2, we have:

rt = (r + 10)(t - 1)

rt = rt - r + 10t - 10

r = 10t - 10 ⟶ Eq. 4

Equating the left hand sides of Eq. 2 and Eq. 3, we have:

(r + 10)(t - 1) = (r - 6)(t + 1)

rt - r + 10t - 10 = rt + r - 6t - 6

16t - 4 = 2r

8t - 2 = r ⟶ Eq. 5

Equating the right hand side of Eq. 4 and the left hand side of Eq. 5, we have:

10t - 10 = 8t - 2

2t = 8

t = 4

Since r = 10t - 10, r = 4(10) - 10 = 30. Finally, since d = rt, d = 30(4) = 120.

Answer: A
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 09 Nov 2019, 00:02
Sarkar93 wrote:
navaneethmmb wrote:
Distance = Speed (s) x time (t)
Case 1: If speed is (s+10), then time taken is (t-1)
Case 2: If speed is (s-6), then time taken is (t+1)

From Case 1,
Distance = st = (s+10)*(t-1) = st - s + 10t -10 Or, s-10t+10 = 0
From Case 2,
Distance = st = (s-6)*(t+1) = st + s - 6t - 6 Or, s - 6t - 6 = 0

Solving the above two equations, we get t = 4 h
Plugging in value of t in the above equations gives s = 30 kmph

Therefore Distance = 30*4 = 120 km

Ans (A)


Can you kindly explain why you equated the two equations in case 1 and case 2 to 0?
Thanks



Hi Sarkar93,

Distance = Speed*Time
Let's say Original Speed = 's' (small s) and Original Time taken = 't' (small t)
It gives Distance = s*t or D = st --> Eq(1)

Case 1 : If Speed increases by 10 kmph, Time taken is reduced by 1 hr.
So, New speed (S) will be = (s+10) and New Time (T) = (t-1)
--> Distance = S*T = (s+10)*(t-1) = (st - s +10t - 10) ---> Eq(2)
--> Notice we have the 'st' component here which is equal to D (from eq.1)

Rewriting the equations we get, D = ST or D = st (where S<>s and T <>t; but ST = st)
(That is, when the Distance remains the same, the Speed and Time can take different sets of values)

Therefore, from Eq.2 --> ST = st - s + 10t -10
Since ST = st, we can cancel them off on either side of the above equation.

That gives us ST - st = (-s+10t-10) or (-s+10t-10) = 0

Hope this clarifies.
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 10 Nov 2019, 06:42
navaneethmmb , ScottTargetTestPrep

Thanks for the detailed explanation. I get it now. Previously, I was ignoring the equation (i), D = S * t in my calculation.
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 12 Nov 2019, 18:44
Sarkar93 wrote:
navaneethmmb , ScottTargetTestPrep

Thanks for the detailed explanation. I get it now. Previously, I was ignoring the equation (i), D = S * t in my calculation.


My pleasure!!
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Jan 2020, 19:55
ScottTargetTestPrep

Hello!

Maybe im a bit tired but I have been reading the problem por a whole hour and I dont understand why cant we equate equations 2 and 3.

Kind regards!
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 06 Jan 2020, 22:54
Bunuel wrote:
A car travelling from city A to B takes an hour lesser to cover the distance if it moved 10 kilometres per hour faster. On the other hand it will take an hour more to cover the distance if it moved 6 kilometres per hour slower. What is the distance between the two cities?

A. 120 kilometres
B. 150 kilometres
C. 180 kilometres
D. 360 kilometres
E. 380 kilometres


Are You Up For the Challenge: 700 Level Questions

Using ST=D equation
according to question
ST = D ------(i)
(S+10)(T-1) = D ------(ii)
(S-6)(T+1) = D -------(iii)

Equating (i) and (ii)
(S+10)(T-1) = ST
S = 10T - 10 -------(iv)

Equating (ii) and (iii)
(S+10)(T-1) = (S-6)(T+1)
S = 8T - 2 -------(v)

from (iv) and (v)
T = 4
S = 30
D = 120

A is correct.
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Re: A car travelling from city A to B takes an hour lesser to cover the di  [#permalink]

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New post 10 Jan 2020, 11:46
jfranciscocuencag wrote:
ScottTargetTestPrep

Hello!

Maybe im a bit tired but I have been reading the problem por a whole hour and I dont understand why cant we equate equations 2 and 3.

Kind regards!



We actually did equate equations 2 and 3; we obtained equation 5 as a result of that.
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Re: A car travelling from city A to B takes an hour lesser to cover the di   [#permalink] 10 Jan 2020, 11:46
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