2013 AMC 8 Problems/Problem 11
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?
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 = 
. For Wednesday, he jogged at a rate of 3 mph. Therefore, 3x = 2 miles. x = 
. On Friday, he jogged at a rate of 4 hours. So, 4x = 2 miles. x=
.
Add the 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 = 
.
To find the amount of time saved: - = 
. To convert this to minutes, use the conversion rate. 
\times $\frac{60}\text{minutes}{1}\text{hour}.$ (Error compiling LaTeX. Unknown error_msg)\boxed{\textbf{(C)}\ 330}$
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| 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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