You ride your bike at an average of 12 miles per hour on the way to school, and at an average of 15 miles per hour on the way home. The total ride time is 22 minutes. How far away is school? Round your answer to the nearest hundredth of a mile
the speeds are in mi/hr, so make sure the total time is expressed in hours, not minutes.
since time = distance/speed,
d/12 + d/15 = 22/60
Now solve for d.
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To find the distance to school, we can use the formula:
Distance = Speed x Time
Let's define some variables:
- Let d be the distance from school.
- Let t1 be the time taken to ride to school.
- Let t2 be the time taken to ride back home.
Given information:
- Average speed on the way to school (t1) = 12 miles per hour
- Average speed on the way back home (t2) = 15 miles per hour
- Total ride time = 22 minutes
We need to convert the total ride time from minutes to hours since the speed is given in miles per hour.
22 minutes = 22/60 hours = 11/30 hours
Now, let's set up the equations:
Equation 1: d = 12*t1
Equation 2: d = 15*t2
Equation 3: t1 + t2 = 11/30
We have two equations (Equations 1 and 2) with two variables (t1 and t2). We can solve this system of equations to find the values of t1 and t2.
From Equation 1, we can express t1 in terms of d: t1 = d/12
From Equation 2, we can express t2 in terms of d: t2 = d/15
Substituting these expressions into Equation 3:
d/12 + d/15 = 11/30
To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators (12, 15, 30), which is 60:
5d + 4d = 22
Combining like terms:
9d = 22
Dividing both sides by 9:
d = 22/9
Rounding the answer to the nearest hundredth of a mile:
d ≈ 2.44 miles
Therefore, the distance to school is approximately 2.44 miles.