SOLUTION: a traveller walks a certain distance. Had he gone half km an hour faster, he would have walked it in four fifth of the time; had he gone half a km an hour slower, he would had been

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Question 1054995: a traveller walks a certain distance. Had he gone half km an hour faster, he would have walked it in four fifth of the time; had he gone half a km an hour slower, he would had been 2.5 hours longer on the road. Find the distance
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you've got 3 equations that need to be solved simultaneously.

they are:

R * T = D

(R + 1/2) * (4/5 * T) = D

(R - 1/2) * (T + 2.5) = D

since all expressions on the left side of each equation are all equal to D, they can all be set equal to each other.

since R * T is easier to deal with, we'll use that as one of the equal pairs.

start with:

R * T = (R + 1/2) * (4/5 * T)

simplify to get:

R * T = 4/5 * R * T + 1/2 * 4/5 * T

divide both sides of this equation by T to get:

R = 4/5 * R + 1/2 * 4/5

subtract 4/5 * R from both sides of this equation to get:

R - 4/5 * R = 4/10

combine like terms to get:

1/5 * R = 4/10

multiply both sides of this equation by 5 to get:

R = 20/10 = 2

now use R * T = D and (R - 1/2) * (T + 2.5) = D

set them equal to each other to get:

R * T = (R - 1/2) * (T + 2.5)

replace R with 2 to get:

2 * T = 3/2 * (T + 2.5)

simplify to get:

2 * T = 3/2 * T + 3/2 * 2.5

subtract 3/2 * T from both sides of this equation to get:

1/2 * T = 3/2 * 2.5

multiply both sides of this equation by 2 to get:

T = 3 * 2.5 which results in T = 7.5

you have R = 2 and T = 7.5

R * T = D becomes 2 * 7.5 = D which results in D = 15.

(R + 1/2) * (4/5 * T) = D becomes 2.5 * 4/5 * 7.5 = D which becomes 2.5 * 30 / 5 = D which becomes 2.5 * 6 = D which results in D = 15.

(R - 1/2) * (T + 2.5) = D becomes 3/2 * 10 = D which results in D = 15.

all 3 equations are satisfied when R = 2 and T = 7.5.

your solution is that the distance is 15 kilometers.