Tourist covered 600km. Every day he would go the same number of kilometers. If the tourist went 10km more every day, then he would travel for 5 days less. How many days did the tourist travel?

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The answer is suppose to be 20 days, but I have no idea how to find it

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Answer 1 · 2015-11-09T14:06:37

#t = 20#

Let #d# be the distance traveled by the tourist every day.
Let #t# be the number of days the tourist traveled to cover 600 km

#600 = dt#

#=> t = 600/d#

If the tourist traveled 10 km more, he'll have to travel 5 days less

#=> t - 5 = 600/(d + 10)#

But #t = 600/d#

#=> 600/d -5 = 600/(d + 10)#

#=> (600 - 5d)/d = 600/(d + 10)#

#=> (600 - 5d)(d + 10) = 600d#

#=> 600d + 6000 - 5d^2 - 50d = 600d#

#=> 6000 - 5d^2 - 50d = 0#

#=> -5d^2 - 50d + 6000 = 0#

#=> d^2 + 10d - 1200 = 0#

#=> (d + 40)(d - 30) = 0#

#=> d = -40, d = 30#

But since we are talking about distance, the value should be positive.

#=> d = 30#

Now, to get the number of days traveled

#t = 600/d#

#=> t = 600/30#

#=> t = 20#