SOLUTION: The distance between two points And B is 100km Two cyclists start simultaneously from A to B.The speed of first cyclist is 10km/hr greater than that of the other. The first cyclist

Question 1064928: The distance between two points And B is 100km Two cyclists start simultaneously from A to B.The speed of first cyclist is 10km/hr greater than that of the other. The first cyclist stops on his way to B and rests for50 minutes but still he is the first to arrive at B. The speed of the first cyclist is
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
At a speed of kph (kilometers per hour),
the second cyclist cover km in
hours.
The second cyclist, at kph,
would cover the same distance in
hours,
but takes a break lasting hours,
so his/her trip takes hours.
The problem says the first cyclist trip took less time,
so is our inequality.
Multiplying both sides of the inequality times
the positive number , we get

Dividing by 5 both sides of the inequality, we get

You know that the quadratic polynomial
is negative only between its zeros.
The solutions to
<--->
are , and ,
and since speeds should not be negative,
---> is the solution.
The second cyclist may be moving at 0 kph (sitting still),
and then the first one would be going at 10kph,
or they both may be moving,
but the first cyclist is moving at
10 kph or more, but less than 40 kph.

RELATED QUESTIONS
The distance between two stations A and B is 300 km. Two motor cyclists start... (answered by mananth)

The distance between two station is 300 km.two motore-cyclists start simultaneously from... (answered by Alan3354)

Two cyclists traveling in opposite directions approach each other. One is moving at 20... (answered by ankor@dixie-net.com)

Two cyclists start at 1:00 P.M. from opposite ends of a 54-mile race course. The average... (answered by richwmiller)

Two cyclists A and B leave X simultaneously at 120� to each other, with constant speeds... (answered by greenestamps)

Two cyclists A and B leave X simultaneously at 120� to each other, with constant speeds... (answered by Fombitz)

Two cyclist start 10 kilometers apart. They are traveling towards each other, cyclist A... (answered by nerdybill)

The distance between two stations A and B is 250 km. Two trains start simultaneously from (answered by richwmiller)

Two town A and B are 300 km apart. C is exacly halfway between A and B. A cyclist departs (answered by ankor@dixie-net.com)