Word problem about distance, rate and time

AI Thread Summary
The discussion revolves around a word problem involving distance, rate, and time, where the equations D = rt are applied. Participants analyze the time taken for different segments of a trip, leading to the conclusion that the total time for the trip must equal the sum of the individual times. A key point of contention is whether a specific equation presented is a typo, with one participant asserting it is not. The clarification emphasizes that the correct relationship should reflect the average speed for the round trip. The conversation highlights the importance of precise mathematical expressions in problem-solving.
paulmdrdo
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Homework Statement



Q35hall_XXIV.jpg

Homework Equations


D = rt

The Attempt at a Solution



I let d to be the total distance

d/3a = t1 ----- time taken for 1st part of the trip

d/3b = t2 ----- time taken for 2nd part of the trip

d/3c = t3 ------ time taken for the whole trip with uniform speed

Since t1+t2 =t3

d/3a + d/3b = d/3c

Multiplying both sides by 3abc

bcd + acd = abd

Dividing both sides by d

bc + ac = ab

Factoring out c and diving both sides by it.

1/c = (a + b)/ab = 1/a + 1/b

1/c = 1/a + 1/b not the same as 2/c =1/a + 1/b

Do you think it is just a typo?[/B]
 
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paulmdrdo said:
d/3c = t3 ------ time taken for the whole trip with uniform speed
Hi Paul:

The problems statement says:
"He could have ridden from A to B and back again in the same time."​
Therefore if t3 = time to go from A to B, then t3 = ( t1 + t2) / 2.

Regards,
Buzz
 
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2/c = 1/a +1/b is a typo. It should be 2/c = 1/a +2/b.
 
paulmdrdo said:
Do you think it is just a typo?
No, it's not a typo.

See what Buzz said.
 

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