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?
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.
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
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?
To solve this problem, we can set up a table or chart to organize the information. The columns should represent the names, rates, times, and distances. Let's set it up:
Names | Rate (mph) | Time (hours) | Distance (miles)
----------------------------------------------------
James | 32 | ? | 186
Tom | 36 | ? | 186
In this case, we need to fill in the missing times for James and Tom.
To find the time, we can use the formula: Time = Distance / Rate.
For James, we know the distance (186 miles) and the rate (32 mph). So, we can calculate James' time as: 186 miles / 32 mph = 5.8125 hours.
For Tom, we know the distance (186 miles) and the rate (36 mph). However, Tom starts 30 minutes (or 0.5 hours) after James. So, we need to subtract the time difference between their starting times. Tom's adjusted time can be calculated as: (186 miles / 36 mph) - 0.5 hours = 4.1667 hours.
Now, let's update our table:
Names | Rate (mph) | Time (hours) | Distance (miles)
----------------------------------------------------
James | 32 | 5.8125 | 186
Tom | 36 | 4.1667 | 186
Since James started at 9:00 AM, we can add his time to get the meeting time. So, 9:00 AM + 5.8125 hours = 2:49 PM.
Therefore, James and Tom met at 2:49 PM.