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Confused by Rate Problems – Can Someone Explain This Step?

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by Neselleept » Wed May 28, 2025 11:13 pm

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Hi everyone,
I’ve been practicing rate/time/distance problems and came across a question that really confused me. Here's the problem:
A car travels from Town A to Town B at 60 mph and returns at 40 mph. What is the car's average speed for the entire trip?
I initially thought the average speed should just be the average of 60 and 40, so 50 mph. But the solution says the correct answer is 48 mph and uses a formula I’m not fully clear on.
Can someone please explain:
Why 50 mph is not correct?
How to approach these types of average speed problems in general?
Thanks in advance!
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Re: Confused by Rate Problems – Can Someone Explain This Step?

by beatthegmat » Thu May 29, 2025 8:51 am
The formula for average speed is:

total distance = (average speed)(total time)

When you travel the same distance at two different speeds, you spend more time at the slower speed (because you are traveling slower and it takes more time to travel that same distance). This means that the value of the average speed for the entire trip will be closer to the slower speed since you spend more time at that slower speed.

As an example, if you travel 120 miles at 60 miles per hour and then travel 120 miles at 40 miles per hour, then that is a total of 120 miles + 120 miles = 240 miles and 2 hours + 3 hours = 5 hours.

(120 miles+120 miles) = (average speed)(2 hours+3 hours)
240 = (average speed)(5)
240/5 = 48 miles per hour = average speed
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