Simultaneous equation

Question

A woman starts walking at 07 00 hrs at a pace of 5km/h. She then rides a bicycle at 25km/h until she reaches a park. In total, she travelled 35km and took 3 hours. Form two simultaneous equations to find the distances she travelled on foot and on the bicycle as well.

Answer 1

distance = rate*time

 

Distance:  If she walks for d km, she rides bicycle for (35-d) km

Time:  If she walks for t hours, she rides bicycle for (3-t) hours

 

Walking:  d = 5t

Bicycling: 35-d = 25(3-t)

 

Using substitution replace d with 5t in equation 2

 

35-5t = 25(3-t)

35 - 5t = 75 - 25t

add 25t to both sides

35 + 20t = 75

subtract 35 from both sides

20t = 40

t = 2 hours walking

3-t = 1 hour bicycling

 

walking distance d = 5t = 10 km

bicycling distance: 35-d = 25 km