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

Question 97985This question is from textbook
: In a bicycle race, Lionel gives Robert a 500m advantage. Also, Lionel agrees to start 15min after Robert. If Lionel bikes at 17km/h and Robert at 14km/h, how long will it take Lionel after he starts biking to overtake Robert?
I already know that you have to convert 500m to 0.5km and 15min to 0.25hours. I have to make an equation out of this but I don't know how. Please help. This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a bicycle race, Lionel gives Robert a 500m advantage. Also, Lionel agrees to start 15min after Robert. If Lionel bikes at 17km/h and Robert at 14km/h, how long will it take Lionel after he starts biking to overtake Robert?
:
When L overtakes R, L will have traveled .5 km further than
:
Let t = travel time for L to overtake R
Then
(t+.25) = travel time of R (had a 15 min head start)
:
Distance = speed * time
:
L's distance = R's distance + .5 (R had a 500 m head start)
17t = 14(t+.25) + .5
:
17t = 14t + 3.5 + .5
:
17t - 14t = 4
:
3t = 4
:
t = 4/3 hr for L to overtake R
:
:
Check the distance of both:
17*(4/3) = 22.68 mi
14*(4/3 + 1/4) = 22.17, .5 mi difference because of the head start
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