SOLUTION: natalie's father started jogging in the park at a speed of 120 metres per minute. 5 minutes later, natalie began to cycle along the same route at 220 metres per minute. how long wo

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: natalie's father started jogging in the park at a speed of 120 metres per minute. 5 minutes later, natalie began to cycle along the same route at 220 metres per minute. how long wo      Log On


   

Question 901244: natalie's father started jogging in the park at a speed of 120 metres per minute. 5 minutes later, natalie began to cycle along the same route at 220 metres per minute. how long would natalie take to catch up with her father?
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
R fast speed, late
r slow speed, early
t time for fast, late
t+k, time for slow, early
d distance when caught-up
UNKNOWNS: t and d

Rule for uniform travel rates, highlight_green%28RATE%2ATIME=DISTANCE%29

______________________speed_________time__________distance
SLOW EARLY____________r_____________t+k___________d=r%28t%2Bk%29
FAST LATE_____________R______________t____________d=Rt

d is for BOTH distances.
r%28t%2Bk%29=Rt
rt%2Brk=Rt
Rt=rt%2Brk
Rt-rt=rk
%28R-r%29t=rK
highlight%28t=%28rk%29%2F%28R-r%29%29

Your problem specifies these values:
r=120, kilometers per minute
R=220, kilometers per minute
k=5, minutes

Evaluate t using the given values.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
natalie's father started jogging in the park at a speed of 120 metres per minute. 5 minutes later, natalie began to cycle along the same route at 220 metres per minute. how long would natalie take to catch up with her father?
***
distance natalie's father traveled in 5 minutes=5*120=600 metres
Relative to her father, natalie speed is 220-120=100 metres/min
travel time=distance/speed=600/100=6 min
how long would natalie take to catch up with her father? 6 min