Linear equations with 2 variables

Question

Boy 1 and boy 2 run 2km twice . In first round boy 1 complete race before 2min then boy 2.In next round boy 2 increases his speed by 2km/hour and boy 1 decreases his speed by 2km/hour,find speed of both boys in 1st round?

Answer 1

Distance = rate x time

 

Boy #1

2 km =  r x 1/30   <---- 2mins = 2/60 hr  = 1/30 hr

 

2 km = (r-2)x t

 

So Boy #1 has speed of 60 km per hour in the first round.

     Boy #1 has speed of 58 km/per hour in the second round, where he will

     complete the 2 km rage is 2/58 hr = 1/29 hr = 1/29 hr x 60 mins/hr = 2 minutes and 4.2 seconds

 

Boy #2

2 km = R x T

 

2 km = (R+2)x T'

 

Subtracting the two equations:

 

    0 = (R+2)*T' - RxT

 

   0 = R * T' + 2 * T' - R x T

 

  -2 * T' = R ( T' - T)

 

-2 * T'

-------  = R where T' is the time it takes boy #2 to complete the 2 km in the second round

T' - T                   T is the time it takes boy #2 to complete the 2 km in the first round