give solution

Question

Two brothers left home for a gym .one brother rode a bicycle at 25.2 km/h to reach the gym 5 min 50 sec later the other brother who took a taxi that drove at 37.8 km/hr .How far was the gym from their home

Answer 1

What you did not say is that they reached the gym at the same time.

 

5 min 50 sec = 5 and 5/6 min = 35/6 min = 35/(6*60) hours =  7/(6*12) = 7/72 hr

 

distance = rate x time

 

            25.2 (t + 7/72) = 37.8 t

 

           25.2 t + 2.45 = 37.8 t

 

              2.45 = 37.8t - 25.2 t

 

            2.45 = 12.6 t

 

            t=0.1944444.... = 0.194 = 11 min 40 seconds

 

 Plugging this into the above equation shows that the distance is 7.35 km

 

 

   

 

           

Answer 2

let x = distance to the gym

 

distance/speed = time

 

the time difference of 5 min 50 sec needs to be converted to an hour by dividing by 60

 

x/25.2 = x/37.8 +  (5 50/60)/60

 

The least common denominator of the first two fractions is 75.6 

 

3x/75.6 = 2x/75.6  + (5/50/60)/60

 

multiply through by 75.6

 

3x = 2x + 7.35

 

x = 7.35

 

7.35 km