Rick rides 11 1/8 miles in an hour with his bike in second gear going uphill. If Rick rides downhill in fourth gear he goes 2 1/2 faster. How many miles will Rick go in an hour downhill in fourth gear?
Well, Rick seems to be quite the adventurer, riding his bike up and down hills! Now, to solve this problem, let's first find out how fast Rick goes uphill.
If Rick rides 11 1/8 miles in an hour uphill, then we can say that his uphill speed is 11 1/8 miles per hour.
Now, we know that when Rick goes downhill in fourth gear, he goes 2 1/2 miles faster. So, we just need to add this speed to his uphill speed.
Adding 2 1/2 to 11 1/8, we get 13 5/8 miles per hour.
So, when Rick rides downhill in fourth gear, he will be going approximately 13 5/8 miles per hour.
To find out how many miles Rick will go downhill in fourth gear, we need to determine how fast he goes uphill in second gear first.
Given that Rick rides 11 1/8 miles in an hour in second gear going uphill, we can set up the following equation:
11 1/8 miles per hour = x miles per hour
To find the value of x, we need to convert the mixed number 11 1/8 miles to an improper fraction.
11 1/8 = (8 x 11 + 1) / 8 = 89/8
So, the equation becomes:
89/8 = x
Now, let's calculate how fast Rick goes downhill in fourth gear by adding 2 1/2 to the speed he goes uphill in second gear.
2 1/2 = 5/2
To find Rick's downhill speed in fourth gear, we can add 5/2 to 89/8:
89/8 + 5/2
To add these fractions, we need to find a common denominator, which is 8 in this case.
(89/8) + (5/2) = (89/8) + (20/8) = (89 + 20) / 8 = 109/8
Therefore, Rick will go 109/8 miles per hour downhill in fourth gear.
To simplify the answer, we can also convert the improper fraction 109/8 to a mixed number:
109 ÷ 8 = 13 remainder 5
The mixed number representation of 109/8 is 13 5/8.
So, Rick will go approximately 13 5/8 miles per hour downhill in fourth gear.
To find out how many miles Rick will go in an hour downhill in fourth gear, we can start by determining his speed going uphill in second gear.
We are given that Rick rides 11 1/8 miles in an hour while going uphill in second gear. This means that his speed in second gear is 11 1/8 miles per hour.
Next, we need to determine how much faster Rick goes downhill in fourth gear. We are told that he goes 2 1/2 miles per hour faster. Therefore, his new speed in fourth gear will be 11 1/8 + 2 1/2 = 13 5/8 miles per hour.
Thus, Rick will go 13 5/8 miles in an hour downhill in fourth gear.
Assuming "...he goes 2 1/2 faster" is meant to say "he goes 2 1/2 times faster".
His downhill speed is therefore
11 1/8 * 2 1/2 = 27 13/16 mph