Hank rides 2 hours total on a bicycle trip into the country and back. He rode out at the rate of 20 mph and returned at the rate of 24 mph. How far into the country did Hank ride
This question has nothing to do with trigonometry. It is algebra.
If D is the one-way distance, in miles,
D/20 + D/24 = 2 hours
The lowest common denominator is 120.
6D/120 + 5D/120 = 11D/120 = 2
D = 240/11 = 21.81 miles
To find the distance Hank rode into the country, we can use the formula:
Distance = Speed × Time
Let's determine the time Hank spent riding into the country and returning.
Let 'x' represent the time it took Hank to ride into the country at a speed of 20 mph.
Since Hank spent a total of 2 hours on the trip, he must have spent (2 - x) hours riding back at a speed of 24 mph.
The distance traveled while going into the country is given by:
Distance into the country = Speed × Time = 20 mph × x hours = 20x miles
The distance traveled while returning is given by:
Distance returning = Speed × Time = 24 mph × (2 - x) hours = 24(2 - x) miles
Since the distance into the country and returning are the same, we can set them equal to each other:
20x = 24(2 - x)
Now, let's solve the equation to find the value of 'x':
20x = 48 - 24x
20x + 24x = 48
44x = 48
x = 48/44
x = 1.09 (rounded to two decimal places)
So, Hank spent approximately 1.09 hours riding into the country.
To find the distance he rode into the country, substitute the value of 'x' into the formula:
Distance = Speed × Time = 20 mph × 1.09 hours ≈ 21.8 miles
Therefore, Hank rode approximately 21.8 miles into the country.