The distance between Sue and a dude ranch was 30 mi. straight accross a rattlsnake-infested canyon. Instead of crossing the canyon, she hiked due north for a long time and then hiked due east for a shorter leg of the journey to the ranch. If she averaged 4 mph and it took her 9 hrs. to get to the ranch, then how far did she hike in a northernly direction? Round your answers to the nearest hundredth.
To determine how far Sue hiked in a northerly direction, we can use the formula:
Distance = Speed × Time
Since Sue traveled at an average speed of 4 mph for a total of 9 hours, we can calculate the distance she traveled in a northerly direction as:
Distance north = Speed × Time north
We know the total distance between Sue and the dude ranch is 30 miles. Let's assume the distance Sue traveled in a northerly direction is 'x' miles.
The distance she hiked due east can be calculated as the difference between the total distance and the distance traveled north:
Distance east = Total distance - Distance north
= 30 miles - x miles
We can now calculate the time Sue spent traveling north:
Time north = Distance north / Speed
= x miles / 4 mph
= x/4 hours
Similarly, we can calculate the time Sue spent traveling east:
Time east = Distance east / Speed
= (30 - x) miles / 4 mph
= (30 - x)/4 hours
Because Sue spent a total of 9 hours on her journey, the sum of the times traveled north and east should equal 9:
Time north + Time east = 9
Substituting the time values:
x/4 + (30 - x)/4 = 9
Now we can solve for 'x':
x + 30 - x = 36
Simplifying,
30 = 36
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