Difference between revisions of "2017 AMC 10B Problems/Problem 2"

Revision as of 22:57, 7 October 2020

Problem

Sofia ran $5$ laps around the $400$ -meter track at her school. For each lap, she ran the first $100$ meters at an average speed of $4$ meters per second and the remaining $300$ meters at an average speed of $5$ meters per second. How much time did Sofia take running the $5$ laps?

$\qquad\textbf{(A)}\ \text{5 minutes and 35 seconds}$
$\qquad\textbf{(B)}\ \text{6 minutes and 40 seconds}$
$\qquad\textbf{(C)}\ \text{7 minutes and 5 seconds}$
$\qquad\textbf{(D)}\ \text{7 minutes and 25 seconds}$
$\qquad\textbf{(E)}\ \text{8 minutes and 10 seconds}$

Solution

If Sofia ran the first $100$ meters of each lap at $4$ meters per second and the remaining $300$ meters of each lap at $5$ meters per second, then she took $\frac{100}{4}+\frac{300}{5}=25+60=85$ seconds for each lap. Because she ran $5$ laps, she took a total of $5 \cdot 85=425$ seconds, or $7$ minutes and $5$ seconds. The answer is $\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}$ .

Video Solution

https://youtu.be/TazCyhFgINI

~savannahsolver

Video Solution by the Beauty of Math / icematrix

With whiteboard at home: https://www.youtube.com/watch?v=zTGuz6EoBWY

~IceMatrix

2017 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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 AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 17: / Line 17: @@
 ~savannahsolver
+==Video Solution by the Beauty of Math / icematrix==
+With whiteboard at home: https://www.youtube.com/watch?v=zTGuz6EoBWY
+~IceMatrix
 ==See Also==
 {{AMC10 box|year=2017|ab=B|num-b=1|num-a=3}}
 {{MAA Notice}}

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