Posted by Lilly on .
Anna and Julia each take a bicycle trip. Anna rides 20 miles in 1 1/3 hours. Julia rides 246 miles in 16 hours. Which has slower unit rate? By how much?

math 
jai,
recall that speed or rate is distance traveled over time, or:
speed, v = d/t
thus, you compare Anna's speed and Julia's speed:
Anna: v = 20/(1 1/3)
Julia: v = 246/(16)
*note: first convert mixed number to improper fraction before dividing.
hope this helps. :) 
math 
Lilly,
so it would e 20/4 over 3? I don't get how I would divide that from 246/16

math 
jai,
it's 20/(4/3),, first simplify this,,

math 
Lilly,
how do you simifly that?

math 
jai,
when dividing a number by a fraction, first get the reciprocal of the fraction,,
*to get reciprocal: you just interchange the numerator and denominator, thus:
reciprocal of 4/3 = 3/4
now the operation becomes multiplication instead of division:
20 * (3/4)
i think you know how to do this. :)
let me see your work. 
math 
Lilly,
which is 12? Then do I divide 12 and 246/16?

math 
jai,
nope, it's not 12,,
remember that a whole number can be written to:
20 = 20/1
now,
20/1 * 3/4 = ?
..and we will not divide the answer by 246/16,, we will just compare them.
first, let me see your answer. 
math 
Lilly,
Well 20 times 3 is 60
1 times 4 is 4
60/4 
math 
jai,
you're on the right track,,
now, what is 60/4 ? 
math 
Lilly,
15/1

math 
jai,
right~! :)
now, we simplify 246/16,,
since the numerator and denominator have a common factor 2, we can cancel it out:
(2*123)/(2*8) = 123/8
123/8 is in simplest form,, now change this to mixed number. 
math 
Lilly,
15 3/8

math 
jai,
yes, that's right~! :)
now comparing the speed:
Anna: 15
Julia: 15 3/8
which of the two is slower (or has smaller speed)?
then, "by how much" means you will get the difference:
15 3/8  15 = ? 
math 
Lilly,
3/8

math 
jai,
nope,, 15 3/8 is greater than 15,,
it's like you have 15 whole pizza plus 3 slices, while the other has only 15 whole pizzas, that's why,
15 3/8 > 15
then, "by how much" means you will get the difference:
15 3/8  15 = ? 
math 
jai,
oh, i see you already have an answer,,
right. the difference is 3/8 m/s. :) 
math 
me,
the answer is obvious, do math