SOLUTION: Hi sam on his way from his house to kukup town after covering 3/8 of his journey, passed a lorry which was traveling at an average speed of 80km per hour. When sam reached his des

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Question 1122044: Hi
sam on his way from his house to kukup town after covering 3/8 of his journey, passed a lorry which was traveling at an average speed of 80km per hour. When sam reached his destination 4 hours later, the lorry was still 60 km from kukup town. If the lorry had started from bay town which was 48km from sams house, how long did the lorry take to travel to kukup town.
thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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sam on his way from his house to kukup town after covering 3/8 of his journey, passed a lorry which was traveling at an average speed of 80km per hour.
When sam reached his destination 4 hours later, the lorry was still 60 km from kukup town.
If the lorry had started from bay town which was 48km from sams house, how long did the lorry take to travel to kukup town.
:
let d = dist from Sam's house to K town
let s = Sam's speed
* Sam passes Lorry (=)
:
..........48.........BayT========*==========......60km....KT
Sam------------3%2F8d---------*------4hr-(5%2F8d)--------KT
:
Sam traveled 5%2F8d in 4hrs
Therefore
%28%285%2F8%29d%29%2Fs = 4
5%2F8d = 4s
5d = 4s * 8
5d = 32s
s = 5d%2F32
s = .15625d
Lorry travels d-108 km while Sam travels d km
distance varies directly with speed
s%2F80 = d%2F%28d-108%29
cross multiply
s(d-108) = 80d
Replace s with .15625d
.15625d(d-108) = 80d
divide both sides by d
.15625(d-108) = 80
.15625d - 16.875 = 80
.15625d = 80 + 16.875
d = 96.875%2F.15625
d = 620 km from Sam's house to K-town
:
"long did the lorry take to travel to kukup town."
620 - 48 = 572 km traveled by the lorry
572%2F80 = 7.15 hrs time for Lorry to travel from Bay-t to Kukup-t