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Chris and Carrie both drive delivery trucks. They leave the warehouse at the same time, but their routes are in opposite directions.
Chris's rate is 20 mph less than Carrie's rate. After 2.5 hours, they are 200 miles apart. What are the rates of the trucks?
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Let x be the Chris rate, in miles per hour.
Then the Carie rate is (x+20) miles per hour.
In 2.5 hours, Chris covered the distance of 2.5x miles.
At the same time, Carrie covered the distance 2.5(x+20) miles.
Since they traveled in opposite directions, the total distance between them is the sum of partial distances
2.5x + 2.5(x+20) = 200.
Simplify and solve for x:
2.5x + 2.5x + 50 = 200
5x = 200 - 50 = 150
x = 150/5 = 30.
Answer. Chris rate is 30 mph; Carrie rate is 30 + 20 = 50 mph.
Check. 2.5*30 + 2.5*50 = 75 + 125 = 200 miles. ! Correct !
Solved.
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See introductory lessons on Travel and Distance problems
- 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.
They are written specially for you.
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.
Become an expert in this area.
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Be aware : The solution by @josgarithmetic is T O T A L L Y W R O N G.
For your safety, simply ignore it.
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@josgarithmetic is VERY well known (or better to say, very badly known, unfortunately) in this forum,
for his inability to solve problems correctly and to make calculations accurately.
So be very careful when you obtain "solutions" from him.
In half of all cases (if not at most cases) they are wrong.
Do not trust him and always wait for reaction of other tutors.
In the normal school environment he would be fired in the second day.
I think about thousands of visitors and students who do understand almost nothing in Math and who were misguided
by his false and wrong quasi- and pseudo-"solutions".
People, be careful about @josgarithmetic ! ! !
@josgarithmetic, go away from the forum !
@josgarithmetic, go away from the forum !
@josgarithmetic, go away from the forum !