A jogger runs from point A to point B at a constant speed of 8 miles per hour and then imm… — GMAT

A jogger runs from point A to point B at a constant speed of $8$ miles per hour and then immediately returns from point B to point A along the exact same route at a constant speed of $12$ miles per hour. If the total time for the entire round trip is $5$ hours, what is the distance, in miles, from point A to point B?

Answer: 24 miles

Answer

The distance from point A to point B is 24 miles.

Let

d

be the distance in miles between point A and point B. The time taken for the outbound journey is

\frac{d}{8}

hours, and the time taken for the return journey is

\frac{d}{12}

hours. Since the total time for the round trip is

5

hours, we set up the equation

\frac{d}{8} + \frac{d}{12} = 5

. Finding a common denominator of

24

, the equation becomes

\frac{3d + 2d}{24} = 5

, which simplifies to

\frac{5d}{24} = 5

. Multiplying both sides by

24

gives

5d = 120

, and dividing by

5

yields

d = 24

miles.

Step-by-Step Solution

Define the variable

d

as the distance in miles between point A and point B, and express the time for each leg of the trip.

Outbound time =

\frac{d}{8}

hours, Return time =

\frac{d}{12}

hours.

Using the fundamental rate formula

t = \frac{d}{r}

, time equals distance divided by speed.

Sum the time spent on the outbound leg and the return leg to match the total round-trip time.

\frac{d}{8} + \frac{d}{12} = 5

The total time for the trip is given as

5

hours.

Find a common denominator to add the algebraic fractions and solve for

d

\frac{3d + 2d}{24} = 5 \implies \frac{5d}{24} = 5 \implies 5d = 120 \implies d = 24

The common denominator of

8

and

12

24

. Simplifying the resulting linear equation yields the one-way distance.

Key Concept

Rate, Time, and Distance Problems:

d = r \cdot t

. Total trip time is the sum of individual leg times (

t_{\text{total}} = t_1 + t_2

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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