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

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Intern
Joined: 03 Mar 2018
Posts: 36
Hayden travels from his home to his office by walking half the distanc [#permalink]

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05 Mar 2018, 07:19
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Question Stats:

73% (00:45) correct 27% (02:29) wrong based on 11 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) $$\frac{4pqrx}{2pq+qr+pr}$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5713
Re: Hayden travels from his home to his office by walking half the distanc [#permalink]

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05 Mar 2018, 07:59
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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Hayden travels from his home to his office by walking half the distanc [#permalink]

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05 Mar 2018, 10:43
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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Hayden travels from his home to his office by walking half the distanc   [#permalink] 05 Mar 2018, 10:43
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