SOLUTION: the question reads: In a bicycle race, Lionel gives Robert a 500 meter advantage. Lionel also agrees to start 15 minutes after Robert. If Lionel bikes at 17 km/h and Robert at 14 k

Question 218393: the question reads: In a bicycle race, Lionel gives Robert a 500 meter advantage. Lionel also agrees to start 15 minutes after Robert. 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?
so I set up a chart:
Time x Rate = Distance
Lionel t+1/4 17 d + 1/2 (km)
Robert t 14 d
then I have the equations:
17(t+1/4) = d + 1/2 and 14t=d
so I solve:
17t + 17/4 = 14t + 1/2
3t = -15/4
and i get t = to a negative number
how is that possible?

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 500 meter advantage. Lionel also agrees to start 15 minutes after Robert. 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?
:
Let's do it this way and then compare what you did
:
Let t = L's travel time
then
(t+.25) = R's travel time
:
A distance equation:
L's dist - .5 km = R's dist
17t - .5 = 14(t+.25)
17t - .5 = 14t + 3.5
17t - 14t = 3.5 + .5
3t = 4
t = hr or 1 hr 20 min for L to catch R
:
:
Check solution by finding the distance each traveled using decimals
17 * 1.33 = 22.6 km
14 * (1.33 +.25) = 22.1 mi
a difference of .5 km
:
:
I think you had L starting before R instead of the other way around.

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