Question

Mr gomez rode to work averaging 45 mi per hour. he averaged 55 MPH on the trip home from work. if he spent a total of 6 hours driving to and from work, how many miles is his work from his home?

Answer 1

lets say his work is x miles away.
then, if he travelled an average of 45 mile per hour going to work, it would take him x/45 hours.
similarly, if he travelled an average of 55 miles per hour coming back home, it would take him x/55 hours.
so we can write:\[\frac{x}{45}+\frac{x}{55}=6\]solve this to find x.

Answer 2

do we cross Multiply?

Answer 3

do you know how to add fractions?

Answer 4

i dont rember no

Answer 5

ok, first you need to find the lowest common multiple (or LCM) of 45 and 55. do you know what that is?

Answer 6

lets start with a simpler fraction problem. lets say we had:\[\frac{1}{3}+\frac{1}{4}\]the first thing we need is the LCM of 3 and 4, do you know what that is?

Answer 7

1?...

Answer 8

no - you need to find the lowest number that is both "multiple" of 3 and a multiple of "4"

Answer 9

2?

Answer 10

e.g.:
3 x 1 = 3 <-- reject as this is NOT a multiple of 4
3 x 2 = 6 <-- reject as this is NOT a multiple of 4
3 x 3 = 9 <-- reject as this is NOT a multiple of 4
3 x 4 = 12 <-- BINGO! this is ALSO a multiple of 4

so 12 is the LCM of 3 and 4

understand?

Answer 11

oh okay... lol

Answer 12

so 495?

Answer 13

so next we can re-write the simpler fraction as:\[\frac{1}{3}+\frac{1}{4}=\frac{1}{3}*\frac{4}{4}+\frac{1}{4}*\frac{3}{3}=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}\]

Answer 14

yes - 495 is the LCM of 45 and 55 - good

Answer 15

so do you think you can do the question now?

Answer 16

yep ive got it now ty

Answer 17

yw