time speed and distance

Question

two trains start at same time form two stations 200 km apart and go in opposite directions on parallel tracks .they cross each other at a distance of 110 km from one of the stations . the ratio of their speeds is:

 

(a)11:20

(b)9:20

(c)11:9

(d)11:10

Answer 1

Hi Vishai,

 

According to what we are told in the problem, we can determine the distance (D) each traveled:

    1.  Faster Train (D) = 110 km

    2.  Slower Train (D) = 90 km

 

If we represent the speed of the faster train as R₁ and the speed of the slower train as R₂ and T as the time traveled by both trains till they met - then we can express the speed of each train by these ratios:

    1.  R₁ = 110 / T (Distance / Time)

    2.  R₂ =  90 / T  (Distance / Time)

 

Now we can determine the ratio of their two speeds by using our expressions for their two speeds:

    R₁/R₂ = (110 / T) / (90 / T)

    R₁/R₂ = 110/90

    R₁/R₂ = 11/9

    R₁:R₂ = 11:9

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.