Question 103893: Doomstown is 200 miles due west of Sagebrush, and Joshua is due west of Doomstown. At 9 A.M. Mr Archer leaves Sagebrush for Joshua. At 1 P.M. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Sassoon travels at an average speed 20 mph faster than Mr Archer and they reach Joshua at 4 pm, how fast is each traveling?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Doomstown is 200 miles due west of Sagebrush, and Joshua is due west of Doomstown. At 9 A.M. Mr Archer leaves Sagebrush for Joshua. At 1 P.M. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Sassoon travels at an average speed 20 mph faster than Mr Archer and they reach Joshua at 4 pm, how fast is each traveling?
:
Josh-----------------d--------------Doom----------------200------------Sage
:
A's travel time: 9am to 4pm = 7 hr
S's travel time: 1pm to 4pm = 3 hr
:
A's speed = s
S's speed = (s+20)
:
Let d = distance from Doom to Josh; (Distance = time * speed)
:
d = 3(s+20); (S's speed times 3 hr)
d = 3s + 60; (use for substitution)
:
(d + 200) = 7s; (A's speed times 7 hrs)
:
In the above equation, Replace d with (3s+60) and find s:
(3s + 60 + 200 = 7s
3s + 260 = 7s
260 = 7s - 3s
260 = 4s
s = 260/4
s = 65 mph is A's speed
Then
65 + 20 = 85 mph is S's speed
:
:
Check solution by finding d
d = 3s + 60
d = 3(65) + 60
d = 195 + 60
d = 255 mi
:
255/85 = 3 hrs S's time
(200+255)/65 = 7 hrs, A's time
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