A man walks one and a half kilometres in one hour. Howmany kilometres

1.	A man walks one and a half kilometres in one hour. Howmany kilometres does he walk in one and a half hours at thisspeed?
Answer» Let r = the rate the man walked then (r+.5) = 1 hr less rate and (r-1) = 3 hr more rate let t = time he actually walked then (t-1) = time taken at the faster speed and (t+3) = time at the slower speed Distance for all three situations is the same (dist = rate * time): So, rt = (r+.5)(t-1) rt = rt - r + .5t - .5 rt - rt + r - .5t = -.5 r - .5t = -.5 (1) Also, for the slower speed case, rt = (r-1)(t+3) rt = rt + 3r -t - 3 rt - rt - 3r + t = -3 -3r + t = -3 (2) multiply the 1st equation by 2 and add to the above equation 2r - t = -1 -3r + t = -3 ---------------eliminates t -r = -4 r = 4 km/h is the actual walking rate Find t using: r -.5t = -.5 4 - .5t = -.5 -.5t = -.5 - 4 -.5t = - 4.5 t = 9 hrs actual time Hence, Dist = rt 4 9 = 36 km

A man walks one and a half kilometres in one hour. Howmany kilometres does he walk in one and a half hours at thisspeed?

Answer»

Let r = the rate the man walked

then (r+.5) = 1 hr less rate

and (r-1) = 3 hr more rate

let t = time he actually walked

then (t-1) = time taken at the faster speed

and (t+3) = time at the slower speed

Distance for all three situations is the same (dist = rate * time):

So, rt = (r+.5)(t-1)

rt = rt - r + .5t - .5

rt - rt + r - .5t = -.5

r - .5t = -.5 (1)

Also, for the slower speed case,

rt = (r-1)(t+3)

rt = rt + 3r -t - 3

rt - rt - 3r + t = -3

-3r + t = -3 (2)

multiply the 1st equation by 2 and add to the above equation

2r - t = -1

-3r + t = -3

---------------eliminates t

-r = -4

r = 4 km/h is the actual walking rate

Find t using: r -.5t = -.5

4 - .5t = -.5

-.5t = -.5 - 4

-.5t = - 4.5

t = 9 hrs actual time

Hence, Dist = r*t

4 * 9 = 36 km