Mark leaves the house for school walking at the rate of 4 kp

Mark leaves the house for school walking at the rate of 4 kph. Two hours later Joyce follows Mark at 4.5 kph. How long will it take Joyce to overtake Mark?

Solution

Mark\'s rate is 4 kph
Mark\'s time time is t+2
Joyce\'s rate is 4.5kph
Joyce\'s time is t
when Joyce overtakes Mark, they will be at the same distance, so we can use the formula rate * time = distance and set their distance = to one another:
4(t+2)=4.5t
4t+8=4.5t
8=.5t
16=t
this makes sense because in 16 hours time, Joyce will has walked 4.5*16 = 72km
and in 18 hours time (he started two hours before her) Mark has walked 4*18=72km