SOLUTION: Ralph took 2.5 minutes to run from point a to point b. Clyde took 2 minutes to run from point a to point b. The faster runner runs 3 feet per second faster than the slower runner

Question 73189: Ralph took 2.5 minutes to run from point a to point b. Clyde took 2 minutes to run from point a to point b. The faster runner runs 3 feet per second faster than the slower runner. Find the speeds of Ralph and Clyde. (make sure to keep the units consistent)
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x= speed (rate) of Ralph, the slower runner (in ft/sec)
Then x+3=speed (rate) of Clyde the faster runner (in ft/sec)
Now we know that:
distance(d)=rate(r) times time(t) or d=rt
Ralph's time was 2.5 minutes or (2.5)(60)=150 seconds (keep units consistent)
Clydes time was 2 minutes or 120 seconds
Now we are told that the boys ran the same distance so:
rate times time for Ralph=rate times time for Clyde or

150x=120(x+3) we are now dealing in ft and seconds--get rid of parens
150x=120x+360 subtract 120x from both sides
150x-120x=120x-120x+360 collect like terms
30x=360 divide both sides by 30
x=12 ft/sec------------------------------------Ralph's speed
x+3=12+3=15 ft/sec-------------------------------Clyde's speed
CK
Ralph's distance=12ft/sec times 150sec=1800 ft
Clyde's distance=15 ft/sec times 120 sec=1800 ft
1800 ft=1800 ft

Hope this helps-----ptaylor

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