Distance rate and time

Question

a man rode his bicycle from his home to the bike shop and then walked back home. he averaged 10km/hr riding and 5 km/hr walking. how far is it from his home to the bicycle shop if his total traveling time was 3 hours

Answer 1

Distance = (Rate)(Time), so Time = Distance/Rate

 

Let x = distance from home to the bike shop

 

Time biking = x/10

 

Time walking = x/5

 

Total time = 3  So, x/10 + x/5 = 3

 

Multiply by the LCD, 10:  x + 2x = 30

 

                                         3x = 30

 

                                          x = 10 km

 

Answer 2

Speed = distance/time

 

let's assume

 

distance = x

 

time for riding bicycle from home to bike shop = y hr

 

time for walking from bike shop to home = 3 - y hr

 

  consider riding

 

speed = distance / time

 

10 =x/y

 

x=10y  ______________  equation 1

 

consider walking

 

speed = distance/time

 

5  = x/3-y

 

x=5(3-y)_____________equation 2

 

we can equate equation 1 and equation 2

 

10y=5(3-y)

 

10y=15-5y

 

15y= 15

 

y = 1

 

substitute y=1 in equation 1

 

x= 10y

 

x= 10(1)

 

x=10

 

distance from home to the bicycle shop = x= 10 km