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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