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Question 117181: Suppose Sashac, a champion bicyclist, wants to see how far he can travel in an hour. He stats timing himself when he reaches a speed of 45 miles/hour. He maintains this speed for 10 minutes. Sascha starts to feel tired and slows down to 30 m/h for the next 5 minutes. He then reduces his speed to 25 m/h for the next 30 minutes. Finally, Sascha feels exhausted as he finishes the last 15 minutes at 15 m / h. I get the average speed he travels is 28.75 but get that he travels only 26.25 and if he travels for an hour it doesn't make sense what did I do wrong. Thanks
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! I'm not sure that I understand your last sentence, but I get a different value for his average speed.
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Use the formula that Distance = Rate times Time
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Or in equation form this is
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The units must be consistent ... D is in miles, R in miles per hour, and T in hours.
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Apply this equation three times ... once for each speed.
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The first application is for the Rate of 45 miles per hour. The Time at this speed is 10 minutes
which is (1/6) of an hour. Substitute these values into the equation and you get:
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So at 45 miles per hour, the distance he travels in ten minutes is 7.5 miles.
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Use the same process when his speed is 30 miles per hour. He travels at that speed for 5 minutes
which is (1/12) of an hour. Substitute these values into the equation and the result is:
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So at 30 miles per hour, the distance he travels in 5 minutes is 2.5 miles.
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Finally, at the speed of 15 miles per hour, for 15 minutes (or 1/4 hour) the distance he
travels is:
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And at 30 miles per hour, the distance he travels in 15 minutes is 3.75 miles.
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Adding up the the distances you get the total distance traveled is:
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 miles
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And the total time it takes to travel that distance is:
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 minutes = 1/2 hour
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The average speed is the total distance (13.75 miles) divided by the time (1/2 hour) which
results in an average speed of:
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 miles per hour
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He covered 13.75 miles in the first 30 minutes. If he rides for the next half hour at an
average speed of 27.5 miles per hour, he will cover 13.75 miles in the second half hour.
So the total distance he will travel is 13.75 miles + 13.75 miles = 27.5 miles, the same distance
he would cover if he just rode at a constant speed of 27.5 miles per hour for 1 hour.
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Does this answer your question? If not, please repost your problem and maybe some other
tutor will see something that I don't in this problem.
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