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# A car first travels uphill at a speed of 54 kmph and then downhill at

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
A car first travels uphill at a speed of 54 kmph and then downhill at  [#permalink]

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06 Jan 2020, 07:40
00:00

Difficulty:

75% (hard)

Question Stats:

56% (02:44) correct 44% (02:02) wrong based on 41 sessions

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A car first travels uphill at a speed of 54 kmph and then downhill at a speed of 72 kmph such that the average speed for the entire journey is 63 kmph. Find the ratio of the uphill distance to the downhill distance.

A. 1 : 1
B. 6 : 7
C. 7 : 8
D. 3 : 4
E. Cannot be determined

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Senior Manager
Joined: 12 Sep 2017
Posts: 316
Re: A car first travels uphill at a speed of 54 kmph and then downhill at  [#permalink]

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14 Jan 2020, 19:24
1
Mine was super time consuming:

Avg.S = Td/Tt

63 = x+y/(x/54 + y/72)

3:4

Can someone please share any short cut?

Kind regards!
Manager
Status: Post MBA, working in the area of Development Finance
Joined: 09 Oct 2006
Posts: 110
Location: Africa
Re: A car first travels uphill at a speed of 54 kmph and then downhill at  [#permalink]

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14 Jan 2020, 23:29
1
jfranciscocuencag wrote:
Mine was super time consuming:

Avg.S = Td/Tt

63 = x+y/(x/54 + y/72)

3:4

Can someone please share any short cut?

Kind regards!

--------------------------------

It would be helpful to remove common factor to ease calculation

So, the equation becomes
7=x+y/(x/6 + y/8)
7*(x/6 + y/8)=x+y
7*(4x + 3y)=24*(x+y)
4x=3y
x/y=3/4
Intern
Joined: 06 Oct 2019
Posts: 3
A car first travels uphill at a speed of 54 kmph and then downhill at  [#permalink]

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15 Jan 2020, 20:28
1
Use weighted average :

Given :
D S T
D1 54 D1/54
D2 72 D2/72

T1/T2 = (Avg - A1)/(A2 - Avg)

(D1/54)/(D2/72) = (63-54)/(72-63) = 9/9 = 1
=> D1/D2 = 3/4
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Re: A car first travels uphill at a speed of 54 kmph and then downhill at  [#permalink]

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21 Jan 2020, 09:50
1
Bunuel wrote:
A car first travels uphill at a speed of 54 kmph and then downhill at a speed of 72 kmph such that the average speed for the entire journey is 63 kmph. Find the ratio of the uphill distance to the downhill distance.

A. 1 : 1
B. 6 : 7
C. 7 : 8
D. 3 : 4
E. Cannot be determined

Let the uphill distance be x and the downhill distance be y (in kilometers). Then, it takes x/54 hours to climb uphill and y/72 hours to travel downhill. Using the average speed formula of total distance/total time, we ger:

(x + y)/(x/54 + y/72) = 63

x + y = 63(x/54 + y/72)

x + y = 63x/54 + 63y/72

x + y = 7x/6 + 7y/8

Multiplying each side by 24, we obtain:

24x + 24y = 4*7x + 3*7y

24x + 24y = 28x + 21y

3y = 4x

x/y = 3/4

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Re: A car first travels uphill at a speed of 54 kmph and then downhill at   [#permalink] 21 Jan 2020, 09:50
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