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 times faster. How many miles will Rick go in an hour downhill in fourth gear?
11.125 * 2.5 = ________ miles
27.81
28 miles
To find out how many miles Rick will go in an hour downhill in fourth gear, we need to calculate the distance he covers uphill first and then multiply it by 2 1/2.
1. Calculate the distance Rick covers uphill:
Rick rides 11 1/8 miles uphill in an hour with his bike in second gear.
2. Convert the mixed number to an improper fraction:
11 1/8 = (8 * 11 + 1) / 8 = 89/8
3. Calculate the distance Rick covers uphill per minute:
To find the distance Rick covers uphill per minute, divide the total distance of 89/8 miles by 60 minutes.
(89/8) miles / 60 minutes = (89/8) / 60 = 89/480
4. Calculate the rate at which Rick rides downhill:
The rate at which Rick rides downhill (in fourth gear) is 2 1/2 times faster than when riding uphill.
Therefore, we need to multiply the distance he covers uphill per minute by 2 1/2.
2 1/2 = 5/2
5. Calculate the distance Rick covers downhill per minute:
Multiply the uphill rate by 5/2:
(89/480) miles/minute * 5/2 = (89 * 5) / (480 * 2) = 445/960
6. Calculate the distance Rick covers downhill in an hour:
To find the distance Rick covers downhill in an hour, multiply the distance per minute by 60.
(445/960) miles/minute * 60 minutes = (445/960) * 60 = 26700/960
7. Simplify the fraction:
Simplifying the fraction 26700/960 gives us: 55 1/2
Therefore, Rick will ride approximately 55 1/2 miles downhill in an hour in fourth gear.