# A cyclist traveled at a constant speed from city A to city B, the distance between which is 60 km. After resting, he went back to A, increasing his speed by 10 km/h. On the way, he made a stop for 3 hours, as a result of which he spent as much time on the way back as on the way from A to B. Find the speed of the cyclist on the way from A to B.

Lucille Douglas 2022-09-14 Answered
A cyclist traveled at a constant speed from city A to city B, the distance between which is 60 km. After resting, he went back to A, increasing his speed by 10 km/h. On the way, he made a stop for 3 hours, as a result of which he spent as much time on the way back as on the way from A to B. Find the speed of the cyclist on the way from A to B.
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Monserrat Ellison

We make an equation:
$\frac{60}{x}=\frac{60}{x+10}+3$
We bring to a common denominator x (x + 10) and discard it, noting that $x\ne 0$ and $x\ne -10$ (and in general x is speed, which means x>0)
60(х+10) = 60х + 3х(х+10)
60х+600=60х+3х2+30х
3х2+30х-600=0 |:3
х2+10х-200=0
D=100+800=900
х(1) = (-10+30)/2 = 10(km/h) - the speed of the cyclist on the way from A to B
х(2)=(-10-30)/2=-20 - does not fit the condition of the problem

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