A delivery truck traveled from Warehouse X to Warehouse Y at a constant speed of 50 miles … — GRE General Test

A delivery truck traveled from Warehouse X to Warehouse Y at a constant speed of $50$ miles per hour. On the return trip along the exact same route, heavy traffic reduced the truck's constant speed to $30$ miles per hour. If the total driving time for the entire round trip was $8$ hours, what was the distance, in miles, between Warehouse X and Warehouse Y?

A
$120$
$150$ Cevap
C
$160$
D
$250$
E
$300$

Cevap

The distance between Warehouse X and Warehouse Y is

150

miles.

The correct distance between the two warehouses is

150

miles. Since time equals distance divided by rate, the time taken going to Warehouse Y is

\frac{d}{50}

hours and returning is

\frac{d}{30}

hours. Summing these expressions to equal the total

8

hours gives

\frac{d}{50} + \frac{d}{30} = 8

. Solving for

d

yields

\frac{8d}{150} = 8

, which simplifies to

d = 150

miles.

Adım Adım Çözüm

Define variables and write time expressions for each leg of the trip

Let

d

be the distance in miles between Warehouse X and Warehouse Y. Time outbound is

t_1 = \frac{d}{50}

hours, and time inbound is

t_2 = \frac{d}{30}

hours.

Distance divided by rate gives the time taken for each individual leg of the journey.

Set up the equation using total elapsed time

\frac{d}{50} + \frac{d}{30} = 8

The total driving time for both legs combined is given as

8

hours.

Solve the algebraic equation for

d

\frac{3d + 5d}{150} = 8 \implies \frac{8d}{150} = 8 \implies 8d = 1200 \implies d = 150

Finding a common denominator of

150

allows combining the fractions to solve for the unknown distance

d

Anahtar Kavram

Distance-Rate-Time Relationship & Harmonic Mean Rate Modeling

Soru

Cevap

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