Travis and Roy own a shipping company that travels 450 miles between Dalls and Pecos.
Suppose Travis leaves Dallas traveling at 55 MPH. After 45 minutes, he notices he forgot the keys to the warehouse he's going to. He calls Roy. Assume Roy leaves immediately when Travis calls him. Roy travels at 65 MPH. Is it possible for Roy to catch up with Travis before he reaches Pecos (a distance of 450 miles)? If he can, how long will it take and how far will they be from Dallas at that time?
2006-11-21 08:43:08 · 6 answers · asked by Jesus 2 in Science & Mathematics ➔ Mathematics
Aaaaaaah. I see what I did wrong.. And I noticed why the 268.125 answer is right! Thanks so much.
2006-11-21 09:17:01 · update #1
Ok. 45 minutes is equal to 3/4 of an hour. To find the distance Travis has travelled at that point in time, you will need to multiply 55 (his rate) by 3/4. That is equal to 41.25 miles. Now we need to find if Roy will ever catch up to him. We are trying to find when their distances are equal, so time can be our variable.
41.25 + 55t = 65 t
41.25 = 10t
t = 4.125 hours
Now, if we plug that in to 41.25 + 55 t and it is greater than 450, then Roy can't reach Travis before Travis reaches Pecos.
41.25 + 55 (4.125) = 268.125
4.125 hours after Roy leaves Dallas, he will catch up to Travis 268.125 miles from Dallas.
2006-11-21 08:54:24 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Travis's distance from Dallis is (starting from the phone call):
d = 55h + 55/(3/4) = 55h + 220/3 in miles
Roy = 65h
So you want to know when Roy and Travis will be in the same place, or same distance from Dallis.
d= Roy
55h + 220/3 = 65h
220/3 = 10h (Because Tavis is ahead by 220/3 miles and each hour Roy catches up by ten miles)
h = 22/3, and plugging that into either of the equations says that d= 22*65/3 = 1430/3 = 476.7 miles
So, no, he will just barely miss it. When Roy catches up, Travis will already be in Pesco.
Good luck.
2006-11-21 16:46:45 · answer #2 · answered by husam 4 · 0⤊ 0⤋
How far has Travis gone when he gets the call? 3/4 of an hour * 55 MPH = 41.25 miles.
Now, Roy is catching up at 10 MPH. So it will take him 4.125 hours to catch up.
In that time, Travis has travelled another 55*4.125 = 226.875 miles. Adding that to his start distance is 268.125 miles, so he will easily catch up.
2006-11-21 16:50:35 · answer #3 · answered by stephen m 4 · 0⤊ 0⤋
When Travis calls Roy, he is 55mph (45min) = 41.25 miles from dallas.
To calculate the time it takes for them to meet we equalize thier distance equations. Travis has a head start so we add an extra 41.25 miles to his distance.
41.25 + 55t = 65t
41.25 = 10t
4.125 hours = t
Then we calculate how far they will be. We can use either Roy's or Travis' distance equation.
65 * 4.125 = 268.125 miles.
So they do catch up.
Thats it!
2006-11-21 16:53:11 · answer #4 · answered by Anonymous · 0⤊ 0⤋
in 45 min at 55mph he has travelled 55*3/4=41.25 mi
the closing speed is 65-55=10 mi/hr
it will tale 41.25/20=4.125 hrs for roy to catch up
in 4.125 hrs at 55mph, Travis will go 226.875 miles for a total of 268.125miles
Roy catches up in 4.125hrs =4hrs 7 min 30sec
they will be 268.125miles from Big D.
2006-11-21 16:50:50 · answer #5 · answered by yupchagee 7 · 0⤊ 0⤋
yes and about 1 hour 7 minutes
2006-11-21 17:01:15 · answer #6 · answered by michaela l 1 · 0⤊ 0⤋