2015 AMC 8 Problems/Problem 17
Contents
Problem
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?
Solutions
Solution 1
Somehow we get and .
This gives , which gives , which then gives .
Solution 2
,
so , plug into the first one and it's miles to school.
Solution 3
We set up an equation in terms of the distance and the speed In miles per hour. We have , giving Hence, .
Solution 4
Since it takes 3/5 of the original time for him to get to school when there is no traffic, the speed must be 5/3 of the speed in no traffic or 2/3 more. Letting x be the rate and we know that 5/3x = x + 18, so we have miles per hour. Solving for x gives us 27 miles per hour. Because minutes is a third of an hour, the distance would then be miles ().
Solution 5
When driving in rush hour traffic, he drives 20 minutes for one distance () to the school. It means he drives 60 minutes for 3 distances () to the school. When driving in no traffic hours, he drives 12 minutes for one distance () to the school. It means he drives 60 minutes for 5 distances () to the school. Comparing these two situations, it gives us , then . So the distance to the school would be miles. ----LarryFlora
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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