SOLUTION: First tourist walked a distance of 30 km in a time 10 minutes shorter than the second tourist. Calculate their speeds if the speed of the first one was 3 km/h greater than that of

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Question 164547: First tourist walked a distance of 30 km in a time 10 minutes shorter than the second tourist. Calculate their speeds if the speed of the first one was 3 km/h greater than that of the second one.
Answer by ptaylor(2198) About Me  (Show Source):
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First tourist walked a distance of 30 km in a time 10 minutes shorter than the second tourist. Calculate their speeds if the speed of the first one was 3 km/h greater than that of the second one.
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Since the problem is dealing in both hours and minutes, we'll just keep it simple and deal in hours
Let t=time it took second tourist to walk 30km
Then t-(1/6)=time it took first tourist to walk 30 km
Rate (speed) of second tourist=30/t
Rate of first tourist=30/(t-(1/6)) and we are told that this is 3 km/hr greater than the speed of the second tourist, so our equation to solve is
(30/(t-(1/6)))-3=30/t multiply each term by t(t-(1/6))
30t-3t(t-(1/6))=30(t-(1/6)) get rid of parens (distributive law)
30t-3t^2+0.5t=30t-5 subtract 30t from and also add 5 to both sides
30t-30t-3t^2+0.5t+5=30t-30t-5+5 collect like terms
-3t^2+0.5t+5=0 multiply each term by -1
3t^2-0.5t-5=0 Quadratic in standard form; solve using the quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%280.5+%2B-+sqrt%28+0.25-4%2A3%2A%28-5%29+%29%29%2F%286%29+
t+=+%280.5+%2B-+sqrt%2860.25%29%29%2F%286%29+
t+=+%280.5+%2B-7.76%29%2F%286%29+
t+=+%280.5+%2B7.76%29%2F%286%29+
t+=+%288.26%29%2F%286%29+
t+=+1.377 hrs----time it took second tourist
t-%281%2F6%29=t-0.167=1.377-0.677=1.21 hrs-----time it took first tourist
rate of second tourist=30/1.377=21.8 km/hr--------------------ans
rate of first tourist=30/1.21=24.8 km/hr------------------------ans
t+=+%280.5+-7.76%29%2F%286%29+ --------------disregard the negative value for t
Hope this helps----ptaylor