SOLUTION: Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his

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Question 1044747: Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min?
Answer by ikleyn(52872) About Me  (Show Source):
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Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic
and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min?
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Let D be the distance under the question.
Then your equation is

D%2F32+%2B+D+%2F48 = 11%2F4.

The first  addend in the left side is the time of driving at 32 mph.
The second addend in the left side is the time of driving at 48 mph.
The right side is the total traveling time, according to the condition.

To solve the equation, multiply both sides by 96, which is LCM of the denominators. You will get

3D + 2D = 120,

5D = 120,

D = 120%2F5 = 24.

Answer. The distance under the question is 24 miles.

Solved.