A commuter drives from home to work at a constant speed of 45 miles per hour and arrives 1… — GMAT

A commuter drives from home to work at a constant speed of $45$ miles per hour and arrives $10$ minutes late. On the following day, driving along the exact same route at a constant speed of $60$ miles per hour, the commuter arrives $5$ minutes early. What is the distance, in miles, from the commuter's home to work?

Answer: 45 miles

Answer

The distance from the commuter's home to work is 45 miles.

Let

d

be the distance in miles between home and work. At

45

miles per hour, the time taken is

\frac{d}{45}

hours. At

60

miles per hour, the time taken is

\frac{d}{60}

hours. The difference between being

10

minutes late and

5

minutes early is

15

minutes, or

\frac{15}{60} = \frac{1}{4}

hour. Setting up the equation

\frac{d}{45} - \frac{d}{60} = \frac{1}{4}

and finding a common denominator of

180

gives

\frac{4d - 3d}{180} = \frac{1}{4}

, which simplifies to

\frac{d}{180} = \frac{1}{4}

. Multiplying both sides by

180

yields

d = 45

miles.

Step-by-Step Solution

Calculate the difference in travel time between the two trips in hours.

The time difference is 10 minutes late - (-5 minutes early) = 15 minutes = 1/4 hour.

Since speeds are given in miles per hour, time must be expressed in hours.

Set up an equation relating the two travel times using the formula time = distance / speed.

d/45 - d/60 = 1/4, where d represents the distance in miles.

The slower speed (45 mph) takes 1/4 hour longer than the faster speed (60 mph).

Solve the equation for the distance variable d.

(4d - 3d)/180 = 1/4 => d/180 = 1/4 => d = 45.

Find a common denominator for 45 and 60, which is 180, and solve for d.

Key Concept

Rate, Time, and Distance Problems

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