Mario walked his dog 5 miles. He walked 3 1/5 miles from home to the post office, and then walked to the library before going home. Mario lives 1 1/2 miles to the library. How far is it from the post office to the library?
5 = 3.2 + (library to PO distance)+ 1.5
= 4.7 + (library to PO distance)
library to PO distance = 0.3 miles
thanks!
To find the distance from the post office to the library, we can subtract the distance Mario walked from home to the post office and the distance from home to the library from the total distance walked.
First, let's calculate the distance Mario walked in total. He walked 3 1/5 miles to the post office, then an additional 1 1/2 miles to the library, and finally he returned home. So, the total distance Mario walked is:
3 1/5 + 1 1/2 + 1 1/2 (returning home) = (3 + 1 + 1) + (1/5 + 1/2 + 1/2)
= 5 + 3/10
= 5 3/10
= 5 1/6 miles
Now, let's subtract the distance from home to the post office and the distance from home to the library from the total distance walked:
Total distance walked - Distance from home to the post office - Distance from home to the library
= 5 1/6 miles - 3 1/5 miles - 1 1/2 miles
To simplify the calculation, we can convert all the mixed numbers into improper fractions:
Total distance walked = 31/6 miles
Distance from home to the post office = 16/5 miles
Distance from home to the library = 3/2 miles
Now, let's substitute the values and calculate:
31/6 - 16/5 - 3/2
To simplify this, we need to find a common denominator. The least common multiple of 6, 5, and 2 is 30.
(31/6)*(5/5) - (16/5)*(6/6) - (3/2)*(15/15)
= 155/30 - 96/30 - 45/30
= (155 - 96 - 45)/30
= 14/30
= 7/15
Therefore, the distance from the post office to the library is 7/15 miles.