SOLUTION: I have been working on this problem for awhile now and I just can't figure it out. I was wondering if someone could help me? I would deeply appreciate it. Please and Thank you!!!

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Question 154027This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this problem for awhile now and I just can't figure it out. I was wondering if someone could help me? I would deeply appreciate it. Please and Thank you!!!
In a bicycle race, Lionel gives Robert a 500m advantage. Also, Lionel agrees to start 15 min 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? This question is from textbook Algebra and Trigonometry Structure and Method book 2

Found 2 solutions by checkley77, nerdybill:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
17(t-.25)=14t
17t-4.25=14t
17t-14t=4.25
3t=4.25
t=4.25/3
t=1.4167 hours Lionel will catch Robert.
proof:
17(1.4167-.25)=14*1.4167
17(1.1667)=19.84
19.83=19.83

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The problem is applying the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let x = time Lionel is traveling
x + .25 = time Robert was traveling
Note: 15 minutes is the same as .25 hour
.
"distance Lionel traveled" = "distance Robert traveled" + .5
Note: 500m is the same as .5 km
.
Our equation then is:
17x = 14(x + .25) + .5
.
Now, we solve for x:
17x = 14x + 3.5 + .5
17x = 14x + 4
3x = 4
x = 4/3
x = 1.333 hours