Difference between revisions of "2011 AMC 10A Problems/Problem 15"
(→Problem 15) |
(→Problem 15) |
||
| Line 1: | Line 1: | ||
== Problem 15 == | == Problem 15 == | ||
| − | Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 40 miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 0.02 gallons per mile. On the whole trip he averaged 55 miles per gallon. How long was the trip in miles? | + | Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first <math>40</math> miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of <math>0.02</math> gallons per mile. On the whole trip he averaged <math>55</math> miles per gallon. How long was the trip in miles? |
<math> | <math> | ||
Revision as of 19:52, 23 November 2016
Problem 15
Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 
miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 
gallons per mile. On the whole trip he averaged 
miles per gallon. How long was the trip in miles?
Solution
We know that 
. Let 
be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is 
. The total distance traveled is 
, so we get 
. Solving this equation, we get 
, so the total distance is 
.
Solution 2
The answer has to be divisble by 55, and the only answer that is divisible by 55 is C. so it's C.
See Also
| 2011 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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. 
