James and tom are in 2 cities which are 186 miles apart and travel towards eachother. James' average rate was 32 mph, and Tom's average ratewas 36mph. If James started at 9:00am and Tom's startes at 9:30 what time did they meet?

Question

I need help settign up the boxes.
SO far I have
Names rate time distance
James 186 miles
Tom 186 miles

Please help, and if you can explain.

Answer 1

looks like your teacher is teaching you how to set up distance-rate-time problems using a chart or "box"
Good Idea!

your chart should have columns labeled Distance, Rate and Time,
It should have two rows, labeled James and Tom

For distance of James put in x miles
for distance of Tom put in 186-x
put in their corresponding speeds.
since Time = distance/speed
James' time = x/32
and Tom's time = (186-x)/36

Don't we know that James drove 1/2 hour longer??
so
x/32 - (186-x)/36 = 1/2
multiply by 288, the LCM
9x - 8(186-x) = 144
solve for x

Answer 2

James travels for t hours
Tom travels for (t - .5 ) hours

James goes 32 t miles
Tom goes 36 (t-.5) = 36 t - 18 miles
so
32 t + 36 t - 18 = 186 miles
got it?