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# Hayden travels from his home to his office by walking half the distanc

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Joined: 03 Mar 2018
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Hayden travels from his home to his office by walking half the distanc  [#permalink]

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05 Mar 2018, 06:19
00:00

Difficulty:

65% (hard)

Question Stats:

67% (00:45) correct 33% (02:21) wrong based on 12 sessions

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Hayden travels from his home to his office by walking half the distance at p miles per hour and cycling the rest distance at q miles per hour. He returns from his office to his home along the same path by a taxi driving at r miles per hour. If Hayden travels for x hours in a day, how many miles does he travel per day?

(A) $$\frac{2pqr}{pq+qr+pr}$$

(B) $$\frac{pqrx}{pq+qr+pr}$$

(C) $$\frac{2pqrx}{2pq+qr+pr}$$

(D) $$\frac{4pqr}{2pq+qr+pr}$$

(E) $$\frac{4pqrx}{2pq+qr+pr}$$

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Re: Hayden travels from his home to his office by walking half the distanc  [#permalink]

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05 Mar 2018, 06:59
itisSheldon wrote:
Hayden travels from his home to his office by walking half the distance at p miles per hour and cycling the rest distance at q miles per hour. He returns from his office to his home along the same path by a taxi driving at r miles per hour. If Hayden travels for x hours in a day, how many miles does he travel per day?

(A) $$\frac{2pqr}{pq+qr+pr}$$

(B) $$\frac{pqrx}{pq+qr+pr}$$

(C) $$\frac{2pqrx}{2pq+qr+pr}$$

(D) $$\frac{4pqr}{2pq+qr+pr}$$

(E) $$\frac{4pqrx}{2pq+qr+pr}$$

let the distance traveled be D..
Hayden travels from his home to his office by walking half the distance at p miles per hour - TIME taken = D/2p
and cycling the rest distance at q miles per hour - TIME taken = D/2q.
He returns from his office to his home along the same path by a taxi driving at r miles per hour- TIME taken = D/r
total time = $$x=\frac{D}{2p}+\frac{D}{2q}+\frac{D}{r}...................D\frac{( qr+pr+2pq)}{2pqr}=x........D=\frac{2pqrx}{qr+pq+2pq}$$
But we are looking for 2D = $$2*\frac{2pqrx}{qr+pq+2pq}$$
E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Hayden travels from his home to his office by walking half the distanc  [#permalink]

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05 Mar 2018, 09:43
Let's assume the distance from home to office be 20 miles, which he takes an hour traveling in the taxi at 20(r) miles/hr
While going to the office, he takes 2 hours walking at 5(p) miles/hr, and the rest of the distance in 1 hour cycling at 10(q) miles/hr

Hence, the total time spent traveling during the day is 1+2+1 = 4 hours and the total distance traveled is 40 km

(A) $$\frac{2pqr}{pq+qr+pr} = \frac{2*5*10*20}{50+200+100} = \frac{2*10*2}{7}$$ - Not an integer

(B) $$\frac{pqrx}{pq+qr+pr} = \frac{5*10*20*4}{50+200+100} = \frac{40*10}{35}$$ - Not at integer

(C) $$\frac{2pqrx}{2pq+qr+pr} = \frac{2*5*10*20*4}{2*50 + 200 + 100} = \frac{10*2*4}{4} = 20$$

(D) $$\frac{4pqr}{2pq+qr+pr} = \frac{4*5*10*20}{400} = 20/2 = 10$$

(E) $$\frac{4pqrx}{2pq+qr+pr} = \frac{4*5*10*20*4}{400} = 40$$ (Option E)

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This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Hayden travels from his home to his office by walking half the distanc &nbs [#permalink] 05 Mar 2018, 09:43
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# Hayden travels from his home to his office by walking half the distanc

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