Others Maths Puzzle

Two cars leave simultaneously from points A and B on the same road in opposite directions. Their speeds are constant, and in the ratio 5 to 4, the car leaving at A being faster. The cars travel to and fro between A and B. They meet for the second time at the 145th milestone and for the third time at the 201st. What milestones are A and B?

Read Solution (Total 1)

Suppose distance between A and B is x miles.
Then

Distance of First meeting point from A = 5x/9
Distance of 2nd meeting point from A = 3x*4/9 -x=3x/9=x/3
Distance of 3rd meeting point from A = 5x*5/9 -2x =7x/9

Distance between 2nd and 3rd meeting points = 7x/9-x/3 = 4x/9 = 201-145=56
x= 56*9/4= 126 miles

Then 2nd meeting point is 3x/9 miles from A.
then A+x/3 =145
A=145-126/3= 145-42= 103 th milestone
B milestone is 103+126 = 229 th milestone.
11 years agoHelpfull: Yes(0) No(0)

Others Other Question

A train leaves a station precisely on the minute, and after having traveled 8 miles, the driver consults his watch and sees the hour-hand is directly over the minute-hand. The average speed over the 8 miles is 33 miles per hour. At what time did the train leave the station? The hour and minute hands of a clock are exactly similar. How many times during the day would it be impossible to tell the correct time?