Difference between revisions of "1957 AHSME Problems/Problem 20"
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− | Suppose the first half of the trip's distance is called <math>x</math>. Then the time for the first half is <math>\dfrac{x}{50},</math> and the second half's time is <math>\dfrac{x}{45}</math>, so the total time is <math>\dfrac{x}{50}+\dfrac{x}{45}</math>, so the speed is <math>\dfrac{2x}{\frac{x}{50}+\frac{x}{45}}=\dfrac{2x}{\frac{19x}{450}}=2x \cdot \dfrac{450}{19x}=\dfrac{900}{19}=47\dfrac{7}{19}</math>, so the answer is <math>\boxed{(A)}</math>. | + | == Problem == |
+ | |||
+ | A man makes a trip by automobile at an average speed of 50 mph. He returns over the same route at an average speed of <math>45</math> mph. | ||
+ | His average speed for the entire trip is: | ||
+ | |||
+ | <math>\textbf{(A)}\ 47\frac{7}{19}\qquad | ||
+ | \textbf{(B)}\ 47\frac{1}{4}\qquad | ||
+ | \textbf{(C)}\ 47\frac{1}{2}\qquad | ||
+ | \textbf{(D)}\ 47\frac{11}{19}\qquad | ||
+ | \textbf{(E)}\ \text{none of these} </math> | ||
+ | |||
+ | == Solution == | ||
+ | Suppose the first half of the trip's distance is called <math>x</math>. Then the time for the first half is <math>\dfrac{x}{50},</math> and the second half's time is <math>\dfrac{x}{45}</math>, so the total time is <math>\dfrac{x}{50}+\dfrac{x}{45}</math>, so the speed is <math>\dfrac{2x}{\frac{x}{50}+\frac{x}{45}}=\dfrac{2x}{\frac{19x}{450}}=2x \cdot \dfrac{450}{19x}=\dfrac{900}{19}=47\dfrac{7}{19}</math>, so the answer is <math>\boxed{\textbf{(A)}}</math>. | ||
+ | |||
+ | == See Also == | ||
+ | {{AHSME 50p box|year=1957|num-b=19|num-a=21}} | ||
+ | {{MAA Notice}} | ||
+ | [[Category:AHSME]][[Category:AHSME Problems]] |
Latest revision as of 09:55, 25 July 2024
Problem
A man makes a trip by automobile at an average speed of 50 mph. He returns over the same route at an average speed of mph.
His average speed for the entire trip is:
Solution
Suppose the first half of the trip's distance is called . Then the time for the first half is
and the second half's time is
, so the total time is
, so the speed is
, so the answer is
.
See Also
1957 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AHSME Problems and Solutions |
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