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Difference between revisions of "1985 AJHSME Problems/Problem 13"

(New page: ==Problem== If you walk for <math>45</math> minutes at a rate of <math>4 \text{ mph}</math> and then run for <math>30</math> minutes at a rate of <math>10\text{ mph}</math>, how many mile...)
 
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==Problem==
 
==Problem==
  
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If you walk for <math>45</math> minutes at a rate of <math>4 \text{ mph}</math> and then run for <math>30</math> minutes at a rate of <math>10\text{ mph}</math>, how many miles will you have gone at the end of one hour and <math>15</math> minutes?
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If you walk for <math>45</math> minutes at a [[rate]] of <math>4 \text{ mph}</math> and then run for <math>30</math> minutes at a rate of <math>10\text{ mph}</math>, how many miles will you have gone at the end of one hour and <math>15</math> minutes?
  
 
<math>\text{(A)}\ 3.5\text{ miles} \qquad \text{(B)}\ 8\text{ miles} \qquad \text{(C)}\ 9\text{ miles} \qquad \text{(D)}\ 25\frac{1}{3}\text{ miles} \qquad \text{(E)}\ 480\text{ miles}</math>
 
<math>\text{(A)}\ 3.5\text{ miles} \qquad \text{(B)}\ 8\text{ miles} \qquad \text{(C)}\ 9\text{ miles} \qquad \text{(D)}\ 25\frac{1}{3}\text{ miles} \qquad \text{(E)}\ 480\text{ miles}</math>
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==See Also==
 
==See Also==
  
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[[1985 AJHSME Problems]]
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{{AJHSME box|year=1985|num-b=12|num-a=14}}
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[[Category:Introductory Algebra Problems]]

Revision as of 20:18, 15 May 2009

Problem

If you walk for $45$ minutes at a rate of $4 \text{ mph}$ and then run for $30$ minutes at a rate of $10\text{ mph}$, how many miles will you have gone at the end of one hour and $15$ minutes?

$\text{(A)}\ 3.5\text{ miles} \qquad \text{(B)}\ 8\text{ miles} \qquad \text{(C)}\ 9\text{ miles} \qquad \text{(D)}\ 25\frac{1}{3}\text{ miles} \qquad \text{(E)}\ 480\text{ miles}$

Solution

$45$ minutes is $\frac{3}{4}$ of an hour, so the walking contributes $\frac{3\text{ hr}}{4}\times \frac{4 \text{ miles}}{1\text{ hr}}=3\text{ miles}$.

Similarly, $30$ minutes is $\frac{1}{2}$ of an hour, so the running adds $\frac{1\text{ hr}}{2}\times\frac{10\text{ miles}}{1\text{ hr}}=5\text{ miles}$.

Their total is $3\text{ miles}+5\text{ miles}=8\text{ miles}$, which is $\boxed{\text{B}}$

See Also

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
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