Question

The bx36 bus comes every 14 minutes.the bx32 bus comes every 4 minutes.both buses arrive at 4:00pm.what time will it be when both buses arrive at the same time again?

Answer 1

Lets make a time table:
Bx36:4:00, 4:14, 4:28
Bx32:4:00, 4:04, 4:08, 4:12, 4:16, 4:20, 4:24, 4:28


The answer is 4:28pm

Answer 2

the number of times bx36 comes is represented by x
the number of times bx32 comes is represented by y

bx36 times (like 1ocloc, 2 o clock etc) it comes is 14x because if it comes once then 14 mins have passed

likewise with bx32 so 4y
so we want to find when 14x=4y
so we try and solve for when x and y are equal
14x=4y
divide both sides by 2
7x=2y
divide both sides by 2
3.5x=y
subsitute a value for x will yield a whole value
if we multiply .5 by 2 then it will yield a whole (nondecimal) value
3.5(2)=7
the first time is when x=2 and y=7 (followed by (x,y)(2,7)(4,14)(6,21))so
if x=2 then 14x=14(2)=28
4:00+28=4:28
4:28 is the next time