I need help in finding the rate.

Question

Luis can run 10 kph faster than Greta. One day,each of them left their house and ran towards each other. If the distance between them was 43.5 km and they met in 45 minutes, what was their rate?

Answer 1

Rate of Greta = x kph

Rate of Luis = x+10 kph

 

distance covered by Greta = d

distance covered by Luis = 43.5 -d

 

time = 45 minute = 45/60 =3/4 =0.75 hr

Speed = distance /time

 

Rate of Luis

 

x+10 = (43.5  -d ) / 0.75

 

0.75x+7.5= 43.5 -d

 

0.75x+d =36 _____________eq 1

 

Rate of Greta

 

x = d/0.75

0.75x =d _________________eq 2

 

substitute d=45x in equation 1

0.75x+d =36

0.75x +0.75x =36

1.5x =36

x =24

 

 

Rate of Greta = x kph=24 kph
Rate of Luis = x+10 kph=24+10 =34kph