SOLUTION: Thor's average driving speed is 25 km/hr faster than Kirk's. In the same length of time it takes Thor to drive 279 km, Kirk only drives 204 km. What is Thor's average speed?

Algebra ->  Test -> SOLUTION: Thor's average driving speed is 25 km/hr faster than Kirk's. In the same length of time it takes Thor to drive 279 km, Kirk only drives 204 km. What is Thor's average speed?      Log On


   

Question 193055: Thor's average driving speed is 25 km/hr faster than Kirk's. In the same length of time it takes Thor to drive 279 km, Kirk only drives 204 km. What is Thor's average speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Two equations for Kirk and Thor:
d%5Bk%5D+=+r%5Bk%5D%2At%5Bk%5D
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
given:
r%5Bt%5D+=+r%5Bk%5D+%2B+25
t%5Bk%5D+=+t%5Bt%5D (I'll call them both t)
d%5Bt%5D+=+279
d%5Bk%5D+=+204
----------------
d%5Bk%5D+=+r%5Bk%5D%2At%5Bk%5D
(1) 204+=+%28r%5Bt%5D+-+25%29%2At
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
(2) 279+=+r%5Bt%5D%2At
From (1):
(1) r%5Bt%5D%2At+-+25t+-+204+=+0
From (2):
(2) r%5Bt%5D%2At+-+279+=+0
Subtract (1) from (2):
25t+-+75+=+0
25t+=+75
t+=+3 hrs
Plug this result into (2)
2) 279+=+r%5Bt%5D%2At
279+=+r%5Bt%5D%2A3
r%5Bt%5D+=+93
Thor's average speed is 93 km/hr
check answer:
(1) 204+=+%28r%5Bt%5D+-+25%29%2At
204+=+%2893+-+25%29%2A3
204+=+68%2A3
204+=+204
OK