A cyclist travels from City X to City Y at a constant speed of 24 miles per hour. On the r… — GRE General Test

A cyclist travels from City $X$ to City $Y$ at a constant speed of $24$ miles per hour. On the return trip from City $Y$ to City $X$ along the exact same route, adverse weather conditions reduce the cyclist's average speed by $25\%$ . If the total time for the entire round trip is $7$ hours, what is the distance, in miles, between City $X$ and City $Y$ ?

A
$73.5$
B
$96$
$72$ Answer
D
$126$
E
$144$

Answer

The distance between City

X

and City

Y

72

miles.

To find the one-way distance

d

, first calculate the return speed:

24 \times 0.75 = 18

mph. Express the total time spent traveling as the sum of the time for each leg:

\frac{d}{24} + \frac{d}{18} = 7

. Combining the fractions over a common denominator of

72

gives

\frac{7d}{72} = 7

, which simplifies to

d = 72

miles.

Step-by-Step Solution

Determine the return speed

Return speed =

24 \times (1 - 0.25) = 18

miles per hour.

Adverse weather reduces the outbound speed of

24

mph by

25\%

Formulate the total time equation in terms of distance

d

\frac{d}{24} + \frac{d}{18} = 7

Time equals distance divided by rate. The sum of the outbound time and return time is

7

hours.

Solve the algebraic equation for

d

\frac{3d + 4d}{72} = 7 \implies \frac{7d}{72} = 7 \implies d = 72

Finding a common denominator of

72

allows combining the fractional time expressions.

Key Concept

Distance, Rate, and Time Word Problems

Estimated Time:1m 30s

Question

Answer

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