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Question

One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bob's was 4 miles per hour, how many miles had Bob walked when they met? The answer is 24, but I don't know how it was calculated. Please help!

Answer 1

stmc left out the time difference. Bob walked 1 hour less time, so if t is the time Yolanda walks,

3t + 4(t-1) = 45
3t + 4t - 4 = 45
7t = 49
t = 7

and so Bob's share of the distance is the 4(t-1) = 4(7-1) = 4(6) = 24.

Answer 2

The word problem is usually solved by translating the words into formulas that can then be turned into an answer.
The problem says that Yolanda and Bob are starting from opposite ends of a path so the total distance they travel is equal to the length of the path when they meet.
I will include many steps that are so obvious that you might do in your head. I have done that because I do not know which step was causing you a problem.

let Ydist=the distance that Yolanda walks to meet Bob.
let Bdist=the distance that Bob walks to meet Yolanda
The first formula is therefore
Ydist+Bdist=45

The problem says that the time that Yolanda walked began to be measured one hour before the time measured of Bob's walk.
Let Ytime=the time that Yolanda walked to meet Bob.
Let Btime=the time that Bob walked to meet Yolanda
The second formula is therefore
Ytime-1=Btime

The problem says that Yolanda walked at 3 miles per hour
The distance that Yolanda walked is the time she walked times the speed she walked.
The third formula is
Ydist=Ytime*3

Likewise Bob who walked at 4 miles per hour traveled speed*time
The fifth formula is
Bdist=Btime*4

Combining the fifth formula and the second formula
The sixth formula is
Bdist=(Ytime-1)*4

Combining The sixth, third and first formulas
The seventh formula is
Ydist+Bdist=Ytime*3+(Ytime-1)*4=45

Combining terms
The eighth formula is
Ytime*7-4=45

adding 4 to each side
Ytime*7=45+4=49

Ytime=49/7=7hours

Ydist=Ytime*3=21Miles
Bdist=45-Ydist=24Miles

Answer 3

the total distance is 45miles, since they walk toward each other, that means they share the distance, when they meet, their distances will add up to 45miles.

x = vt (yolanda)
x = vt = (bob)

vt(yolanda) + vt(bob) = 45
3t + 4t = 45
7t = 45
t = 6.43hr

use the time we just found to find the distance
x=vt
x = (4)(6.43)
x= 25.68miles

i don't know how they got 24 miles. Perhaps, they only take 6hr instead of 6.43hr for the time

if they do, then the asnwer is 24miles

Answer 4

first figure the time is takes for Yolanda and Bob to meet:
yolanda had a one hour head start, so 3 miles is added to herside of the equation:

(3mph)t+3mi +(4mph)t= 45 mi
(7mph)(t hrs) = 42hrs
t = 6 hours
now find out how far Bob travels in 6 hours

4mph(6h) = 24 mi