SOLUTION: In a bicylce race, Lionel gives Robert a 500 m advantafe. Also, Lionel agrees to start 15 min after Rivert. If Lionel bikes at 17 km/h and Robert at 14 km/h, how long will it take

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Question 155496: In a bicylce race, Lionel gives Robert a 500 m advantafe. Also, Lionel agrees to start 15 min after Rivert. If Lionel bikes at 17 km/h and Robert at 14 km/h, how long will it take lionel after he starts biking to overtake Robert?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a bicycle race, Lionel gives Robert a 500 m advantage. Also, Lionel agrees to start 15 min after Rivert. If Lionel bikes at 17 km/h and Robert at 14 km/h, how long will it take Lionel after he starts biking to overtake Robert?
:
Convert 500m to km: = .5 km
Convert 15 min to hrs: = .25 hrs
:
Let t = time for L to overtake R
:
Write a dist equation: Dist = speed * speed
:
L's dist = R's dist + .5 km + dist in .25 hr
16t = 14t + .5 + (.25*14)
:
16t = 14t + .5 + 3.5
:
16t - 14t = 4
:
3t = 4
t = 4%2F3
t = 11%2F3 hrs for L to catch R
:
:
Check by finding the distance:
1.33*17 = 22.61
1.33*14 = 18.62
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differs = 3.99 ~ 4 km head-start to be overcome by L