SOLUTION: Jenna and Caleb are having a go-kart race. Jenna's go kart is traveling 10 mph while Caleb's is only going 8 mph. If Caleb gets a 1/10 mile head start, how many minutes will it tak

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Jenna and Caleb are having a go-kart race. Jenna's go kart is traveling 10 mph while Caleb's is only going 8 mph. If Caleb gets a 1/10 mile head start, how many minutes will it tak      Log On

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Question 209589: Jenna and Caleb are having a go-kart race. Jenna's go kart is traveling 10 mph while Caleb's is only going 8 mph. If Caleb gets a 1/10 mile head start, how many minutes will it take Jenna to catch him?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Each person has their own equation
For Jenna:
d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
For Caleb:
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
given:
r%5Bj%5D+=+10 mi/hr
r%5Bc%5D+=+8 mi/hr
t%5Bj%5D+=+t%5Bc%5D hr (I'll call them both t)
d%5Bj%5D+=+d%5Bc%5D+%2B+.1
Notice that they both start at the same time
and they finish at the same time.
And also, Jenna has to go 1/10 mi further
---------------------
Now I can rewrite their equations
d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
d%5Bc%5D+%2B+.1+=+10t
and
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
d%5Bc%5D+=+8t
By substitution,
8t+%2B+.1+=+10t
2t+=+.1
t+=+.05 hr
Converting to minutes:
.05%2A60+=+3 min
It will take Jenna 3 minutes to catch him
check answer:
d%5Bc%5D+%2B+.1+=+10t
d%5Bc%5D+=+10%2A.05+-+.1
d%5Bc%5D+=+.5+-+.1
d%5Bc%5D+=+.4 mi
and
d%5Bj%5D+=+10t
d%5Bj%5D+=+10%2A.05
d%5Bj%5D+=+.5 mi
This shows Caleb has .5+-+.4+=+.1 headstart
OK