SOLUTION: A man started driving his car at a certain time from a certain place. On arrival at his destination at the precise appointed time, he said, "If I had averaged 6 miles per hour fast

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Question 939602: A man started driving his car at a certain time from a certain place. On arrival at his destination at the precise appointed time, he said, "If I had averaged 6 miles per hour faster, I would have been 5 minutes early. But if I had averaged 5 mph slower, I would have been 6 minutes late." Find how far he had driven.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
___________________rate_____________time_____________distance
Faster_____________r+6_____________t-5/60____________d
OnTime______________r_______________t________________d
Slower_____________r-5____________t+6/60_____________d

Three equations using three unknowns, r, t, d.
Goal is find the value for d.

system%28%28r%2B6%29%28t-1%2F12%29=d%2Crt=d%2C%28r-5%29%28t%2B1%2F10%29=d%29

system%28rt%2B6t-r%2F12-1%2F2=d%2Crt=d%2Crt-5t%2Br%2F10-1%2F2=d%29

Use the simpler equation to substitute for rt in the Fast and Slow equations, and simplify. If you handle this correctly then you get a system of two equations in r and t. Solve that system for r and t... and you can then evaluate r*t=d.