2019 AMC 8 Problems/Problem 16
Contents
Problem 16
Qiang drives miles at an average speed of
miles per hour. How many additional miles will he have to drive at
miles per hour to average
miles per hour for the entire trip?
Solution 1
The only option that is easily divisible by is
, which gives 2 hours of travel. And, the formula is
.
And, =
.
Thus, .
Both are equal and thus our answer is
Solution 2
To calculate the average speed, simply evaluate the total distance over the total time. Let the number of additional miles he has to drive be Therefore, the total distance is
and the total time (in hours) is
We can set up the following equation:
Simplifying the equation, we get
Solving the equation yields
so our answer is
.
Solution 3
If he travels miles at a speed of
miles per hour, he travels for 30 min. Average rate is total distance over total time so
, where d is the distance left to travel and t is the time to travel that distance. Solve for
to get
. You also know that he has to travel
miles per hour for some time, so
. Plug that in for d to get
and
and since
,
, the answer is
.
Video Solution
Associated Video - https://www.youtube.com/watch?v=OC1KdFeZFeE
https://youtu.be/5K1AgeZ8rUQ - happytwin
https://www.youtube.com/watch?v=0rcDe2bDRug
Video Solution
Solution detailing how to solve the problem: https://www.youtube.com/watch?v=sEZ0sM-d1FA&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=17
Video Solution
https://youtu.be/aFsC5awOWBk Soo, DRMS, NM
Video Solution
~savannahsolver
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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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