2013 AMC 8 Problems/Problem 11

Revision as of 18:06, 27 November 2013 by Arpanliku (talk | contribs) (Solution)

Problem

Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. How many minutes less?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Solution

You have to find the hours spent on each day. For people who do not know how to do this, here is a slower way to do it (you will be able to do quickly once you learn it):

On Monday, he was at a rate of 5 mph. So, 5x = 2 miles. x = $\frac{2}{5} hours$. For Wednesday, he jogged at a rate of 3 mph. Therefore, 3x = 2 miles. x = $\frac{2}{3} hours$. On Friday, he jogged at a rate of 4 hours. So, 4x = 2 miles. x=$\frac{2}{4} hours$.

Add the hours = $\frac{2}{5} hours$ + $\frac{2}{3} hours$ + $\frac{2}{4} hours$ = $\frac{94}{60} hours$.

Once you find this, answer the actual question by finding the amount of time Grandfather would take by jogging at 4 mph per day. Set up the equation, 4x = 2 miles \times 3 days. x = $\frac{3}{2} hours$.

To find the amount of time saved: $\frac{94}{60} hours$ - $\frac{3}{2} hours$ = $\frac{4}{60} hours$. To convert this to minutes, use the conversion rate. $\frac{4}{60} hours$ \times $\frac{60  minutes}{1  hour}.$\boxed{\textbf{(C)}\ 330}$

See Also

2013 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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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