Question 1126120: Need help please. I don't know how to set this problem up. I wish my text did a better job explaining, but here I am.
Greg left Mark's house and traveled toward the mountains. Two hours later Fred left Mark's house traveling 18 MPH faster in an effort to catch up. After three hours Fred finally caught up. What was Greg's average speed?
Thank you in advance for any help provided!
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the general formula to use is rate * time = distance.
let R = the rate and T equal the time and D = the distance and the formula becomes R * T = D.
greg
the formula for greg is R * T = D
fred leave 2 hours later and travels 18 miles per hour faster and catches up with greg 3 hours later.
when fred catches up with greg, he has traveled 3 hours and greg has traveled 5 hours because greg left 2 hours earlier.
when fred catches up with greg, they both have traveled the same distance.
the formula for greg becomes R * 5 = D
the formula for fred becomes (R + 18) * 3 = D
these two equations need to be solved simultaneously and your primary goal is to solve for R.
since R * 5 = D from the first equation, you can replace D with R * 5 in the second equaiton to get:
(R + 18) * 3 = D becomes (R + 18) * 3 = R * 5
simplify to get 3R + 54 = 5R.
subtract 3R from both sides of the equation to get 54 = 2R.
solve for R to get R = 27.
for greg, 5 * R = D becomes 5 * 27 = D which becomes D = 135.
for fred, 3 * (R + 18) = D becomes 3R + 54 = D which becomes 3 * 27 + 54 = D which becomes 81 + 54 = D which becomes D = 135.
they both traveled the same distance.
greg did it in 5 hours traveling at 27 miles per hour.
fred did it in 3 hours traveling at 27 + 18 = 45 miles per hour.
your solution is that greg was traveling at 27 miles per hour.
this is the way i solve them.
if there's a better way, i don't know it.
i always use the basic formula of rate * time = distance and then adjust it accordingly.
some logic needs to be applied, such as greg must have been traveling 2 more hours than fred, so if fred caught up with greg after 3 hours, then greg must have been traveling for 5, and when fred catches up with greg, they both had to have been traveling the same distance, and, if greg is traveling at R miles per hour, then fred must have been traveling at R + 18 miles per hour.
analyzing this way takes a few times to get used to, and i don't always get it right the first time, but after a while it becomes more comfortable to do it this way, and i have been successful with the method most of the time.
Answer by ikleyn(52780)  (Show Source):
You can put this solution on YOUR website! .
Let x be the Greg's average spreed.
Greg traveled 2 + 3 = 5 hours and covered 5x miles before Fred caught him.
Fred traveled 3 hours at the speed (x+18) miles per hour; hence, Fred traveled 3*x miles.
The distance each of them traveled from the start to the caught point is the same,
which gives you an equation
5x = 3*(x+18).
This is the central moment in setup.
As soon as you got it and as soon as you understood how you got it, the setup is done.
The solution is very easy:
5x = 3x + 54 ====> 5x - 3x = 54 ====> 2x = 54 ====x = 54/2 = 27.
Answer. The Greg's average speed was 27 miles per hour.
Solved.
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- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
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You will find the solutions of many similar problems there.
Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.
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